That's an interesting theory, and one worth exploring. Certainly, I think AA, or the Last Hero, or any of the other figures who fill that role, was a greenseer, may have been involved in some form of reanimation, and may very well have been an undead greenseer. I also have some suspicions about greenseers warging other greenseers (or at least greenseers warging wargs), and suspect that may describe how the Others operate on some level.
Personally, I think too much greenseer blood was sacrificed to create the Three-Eyed Crow entity/conciousness. There simply wasn't/isn't enough left to man a Watch composed of undead greenseers. And beyond that, it appears the Night's Watch was intimately involved in some sort of scheme to transport bastard born children (likely carrying the holy blood line) north of the Wall for sacrifice.
I have another theory that this may have been their original purpose; to maintain the holy blood line (ie the greenseer gene/genes), as a gardener might maintain a plant. Ensure that the blood line remains intact, while pruning any superfluous offshoots. I can think of several reasons why they might engage in either the former or the latter, but one reason shared equally by both objectives is to "guard the realms of men."
This leads me to an image in my head of the Night's Watch guarding the walls of every (major) castle in Westeros, like a militant version of the maesters, watching primarily for people trying to sneak away with bastard born children. Certainly, an agreement (maybe the Pact, maybe another) which included the provision of bastard born children would be a strong motivator to develop and/or adopt jus prima noctis. And consequently, any push to ban the practice would indicate both a break from traditional practices, as well as an answer to one of the overarching questions of ASOIAF, why now? As in, why are the Others becoming (significantly) more active now. More broadly, what happened to uppend an apparent balance which it seems lasted for thousands of years.
The answer is not going to be so obviously simple as Good Queen Alyssane happened, but the visit to the Wall (with dragons, no less), and the push to ban jus prima noctis, both stand out to me as red flags. The visit itself seems in some way connected to Bael the Bard, whose exploits likely took place during the reign of Jaehearys I. We're also supplied with some indication that this is a possible moment when the Night's Watch changed its vows to include the additional statements about not marrying, fathering children, holding land, etc.
At the very least, there's something off about Snowgate being renamed Queensgate, when the Queen paid for the construction of Deep Lake. Typically, the structure whose construction is funded by a singularly noteworthy donor is the one named after that donor; I can't say I've heard of so generous a gift being met so poorly. It suggests to me that the primary motivator for the name change may have been the commander of Snowgate, or Alyssane herself; either way, there's a connection between the renaming and the Snow in Snowgate.
I also have to wonder why there was a fairly sizeable gap between the Nightfort and Snowgate, when all the other fortifications seem to be built at roughly even intervals of distance. The gap was so sizeable that they could drop Deep Lake in roughly equidistant from the two nearest fortifications, and it seems to fit right in as though it had always existed there. On some level, it makes me wonder if there wasn't an earlier fortification at the site of Deep Lake.
I would need to track down the quote, but in one of the books, Sam tells us that 600 years prior, the commanders of the Nightfort and Snowgate declared war on eachother (edit: actually, I think it's two books, as I think this story is part of the infamous 'list of Lord Commanders' speech we read twice). His story continues, with the Lord Commander of the Night's Watch stepping in to settle the agreement. We can immediately conclude that as far back as 600 years ago, the Night's Watch had already moved its headquarters from the Nightfort to Castle Black.
This indicates that the secret at the heart of the Night's Watch, namely whatever the story is regarding the full weirwood tree they built the Nightfort over, had already been forgotten. This is why I say above that "the answer is not going to be so obviously simple as Good Queen Alyssane happened." The traditions had already been forgotten by the time Alyssane visited the Wall, and indeed were probably forgotten or abandoned in bits and pieces over centuries. Alyssane merely enacted a rule change which undermined any (un)official return to a practice that may very well have been all that was keeping the peace between the Others and the rest of the world.
We can also conclude that the Lord Commander during this conflict 600 years ago was likely an Andal, as the story concludes with the commanders of the Nightfort and Snowgate joining to assassinate the Lord Commander. That sounds to me like some Northerners getting into a brawl, and only ending their fight when an outsider presented himself as both an obstacle and target.
I know this is a long post already, but there were two more thoughts I want to get out there before I promptly end it.
Yes, I adhere to a literal interpretation of Bran's impaled dreamer vision. As a real location/object, it works equally well as the literary device most fans restrict it to being. Further, there's no evidence in the description of the impaled dreamers to suggest it's not real; namely, they're not impaled shadows. This is important, as George gives us the description of "visionary" figures, ie the shadows Bran sees earlier in this same dream, as well as the shadows Dany sees in the ritual tent. Further, we have good reason to doubt that failed dreamers are impaled, literally or metaphorically, as we see no evidence of such with Euron, who seems to be a failed candidate. He is neither dead (as far as we know), nor does his third eye seem permanently locked.
Finally, and I don't mean this to be offensive to anyone who does support the following theory, it's extremely unlikely the weirwood underneath the Nightfort (really, the weirwood the Nightfort was built on top of) is connected to the weirwood at Whitetree. First, if I recall correctly, Whitetree has moved, from north of the Nightfort in earlier books, to north of Deep Lake in more recent maps I've seen. Beyond that, George's description is plainly of a buried tree; specifically, what is confused for its trunk is merely a branch, hence it being thin, twisted, and reaching. This description, to me, is so obviously of a buried tree I'm somewhat amazed that no ASOIAF theory I've read has correctly identified it as such. Also, I don't see why anyone would want to devalue the Nightfort by making it an extension of Whitetree.
If anything, I feel Whitetree is meant to serve as our mental template for the tree underneath the Nightfort. If the tree at Whitetree is large and monsterous, the tree beneath the Nightfort is likely that much further beyond the Whitetree as the Whitetree is to other weirwoods. In fact, the Nightfort tree is so wild and crazy, it even has an interactive face (edit: in re-reading this, I have to wonder if that's Bran's face in the Nightfort tree; it would certainly add tremendous significance to the image of the baptismal tear shed by the tree, even if the "tear" is indicative of the presence of salt water in the Wall).
I know I said only two more, but I thought of a third; if the Pact was thousands of years ago, and the Children fled north of the Wall thousands of years ago, and mankind cut down all the weirwoods south of the Neck thousands of years ago, where did Harren find numerous weirwoods to chop down and use for the construction of Harrenhal? And, why would he leave the closest weirwood standing? Even if my last assumption is incorrect, that mankind cut down all weirwoods south of the Neck thousands of years ago,I have difficulty reconciling that so many weirwoods were still standing.
And, am I the only one seeing parallels between the desecration of numerous weirwoods which it seems prompted the Pact, the construction of Harrenhal which required the desecration of numerous weirwoods, the rise of Night's King ~100 years after the formation of the Watch, and Alyssane's visit to the Wall, which resulted in a doubling of the Night's Watch's lands ~100 years after Aegon's Conquest.
It has been discussed on this sub-forum that the Age of Heroes, the Long Night, etc., all happened much more recently than the ubiquitous 10,000 years ago, 8,000 years ago, or "thousands and thousands" of years ago. I'm personally looking at a Long Night which took place ~5,000 years ago, and I'm even open to a further condensed timeline, but on some level I keep coming back to the idea that 200-300 years is easily enough time for a society to have forgotten something important, and even something as important as the details of Long Night and its resolution, assuming a society even had those answers in the first place.
This isn't actually consistent with George's references to a written history dating back thousands of years, but outside of Sam's "600 years ago" story, I can't say I've seen much which is even that accurately dated. During what, Sam? You were obviously going to connect that list to a specific period in history (correctly or incorrectly). If the list represents something like 5,000-5,500 years, what was going on that Sam could attribute it to "during...."
Well, beyond the obvious, like the rise of Valyria and its dragons, the fall of (Old) Ghis and its harpies, and the possible origin of the AAR prophecy.