Why did Criston Cole support Aegon II?

[Jaak]

18 hours ago, Lord Varys said:

Well, it is clear that the man did not want to rule, right? I mean, that should be the main reason why he resigned as Hand on the same day he took the office.

It´s not clear he did not want to rule. Mayhaps he wanted to rule, but not lose in fighting the whole Westeros, Black and Green, united against him. Or mayhaps he did want to rule, but not with compromises necessary to keep the rule... so his offer of compromise was go back North with some heads.

18 hours ago, Lord Varys said:

The Martells want revenge for Elia and the children. Not for Aerys. And Jaime only killed Aerys. But keep in mind that I spoke about the Lords of the West, not the Lannisters. Aegon very well could win the allegiance for a majority of the bannermen of House Lannister without granting the Lannisters any favors. 

And there are the non-Tywin branches around to spare. Martyn, Damon, Daven...

18 hours ago, Lord Varys said:

I also not said that some common men/second-tier officers should be rewarded with lordships. Castles and titles should go to the officers, meaning first to Strickland and then to Black Balaq, Garys Edoryen, Lysono Maar, and then to the other captains. I guess some of the other captains and officers might get rewards, too, and even some of the common men if they prove their loyalty in battle.

After Blackwater, there were 47 lordships forfeited. And 600+ "landed" knights - many of whom would have had castles. (Are landed knights without castles and with unfortified halls present in Westeros?)

18 hours ago, Lord Varys said:

The idea that the Golden Company expect that Aegon is going to grant them all of Westeros or some ancestral seats they claim are theirs is not very likely, though. The Peake castles aside from Starpike might no longer exist, by the way. They have never been mentioned in the books as of yet. The same might go for Coldmoat.

They might not be castles. Does not mean the location does not exist.

How much do you think would Riverlands lords and smallfolk be required to spend this winter to rebuild Oldstones in a style appropriate to Lord Paramount Mudd? And was it named "Oldstones" when Mudds first built it?