What is the point of time-travel...

[Ser Yorick Ampersand]

...If you can't change the past?

[The hairy bear]

If you meant it as a philosophical question, then the answer is knowledge and entertainment. Wouldn't we love to be able to see the battle of Gaugamela, or read the lost works from the library of Alexandria? Wouldn't it be thrilling to watch the discovery of fire or the wheel?

I you you are referring to the purpose as a storytelling device, I guess that it's a way of "showing not telling", and reveal information about situations where all the protagonists are now dead.

 

[UnmaskedLurker]

In the GoT world, time travel simply is what it is -- it is not there for any "purpose" per se -- it just happens to exist the way it does. So Bran and 3ER time travel because they can -- they want to know about the past and what happened. Bran's effect on the past was not really intentional -- it was merely the consequence of his actions.

Now if you mean why did GRRM (I am assuming it will work the same in the books) decide to use this form of time travel rather than the more common form where the past can be change -- I think it is because this form is WAY cooler. I am not a big fan of traditional time travel. Nothing that happens in the story really matters because it can all be undone through time travel. So what is really at stake? In this version of time travel, we see the events or their aftermath (like seeing the effects of Hodor being Hodor -- and then finding out later that he is only Hodor because Bran had time traveled and affected the past). So this use of time travel end up being a much more limited affect on the story -- but a more interesting effect (at least for me).

I hope that gives you some insight into why this form of time travel exists in GoT. If I misunderstood your question, however, please clarify and I will try to give it a go at answering. 

[Greg B]

The ability to access different periods in a fixed timeline regardless of the observer's own location on the timeline enables real prophecy and divination magic, and empowers the themes of fate and destiny that seem to be at the heart of the "Song of Ice and Fire." It's therefore crucial to the world-building and story-crafting, in my opinion, though Bran's ability to go back and look at the past (or to create a causal loop) is more of a side-effect or implication of this characteristic of the world than the underlying point of it from a narrative persepctive.