Hmm, rifts... Well, I definitely dislike that they're all so isolated and only produce demons when you approach them. I would have loved to see demons roaming around the areas near them, giving you a motivation to close them and adding a slightly dynamic environment. It's also puzzling why there are none near populated areas that attack said populated areas, giving you even more reason to close them. Even the ones that are fairly close don't produce demons, as said before. I remember frantically trying to save towns from dragons in Skyrim, and would have liked to save them from demons (and dragons, for that matter) in DA:I. Actually, that makes me realize I have similar thoughts about the dragons in this game. They sort of just wait for you to attack them. It would have been cooler if they ambushed you or attacked keeps, especially.
Gameplay-wise, rifts are alright and I don't mind the random demons. One thing that does disappoint me though, is their health meter. And by that I mean the fact that it's useless because every rift I can remember simply has two waves. Even on Nightmare! How boring and predictable! Why not have some lowly rifts that can close after the initial demons are dealt with? Why not some with a few waves, since there are barely any long fights in DA:I? Come to think of it, why can't you close them while demons are there? Do they force it open somehow? If I designed rifts, I think I would have them spawn a lot of enemies gradually in addition to the initial wave (but not infinite), encouraging you to close it during combat, which would be harder.
I also hate how they reset if you go "too far" away, like you said. The range isn't very far, and sometimes I'll end up in a hard fight and Varric will be near the edge of the invisible zone, naturally, and he'll use Leaping Shot and I'll have to fight those Pride Demons all over again
Couldn't they have just made the demons follow you a little? Those are my thoughts on rifts I guess.