Amaurot: Why there? (Spoilers ShB and EW)

[Iscah]

There seem to have been a couple of factors.

Firstly the genuine ruins are there, while apparently they may no longer exist in the Source due to extra disturbance from the various calamities. If he's going to hide out somewhere in the First, it might as well be "home".

Additionally, it's noted that he can't afford to flee into the rift while he holds the Exarch captive, so he does have to stay in the First for now.

And of course the First is also where the WoL is right now, and the whole illusion is for their benefit – and he wants the WoL to unleash all that Light energy back into the First if they can't control it, so there's no point sending them elsewhere.

I also don't think, at a story level, we're really supposed to be able to freely teleport between worlds. Aside of the specific dialogue explaining why we can still teleport (which may simply be for gameplay's sake, as they can't functionally hold up our access to other parts of the game), everything else points to us being semi-permanently in the First once summoned: we send messages back via Feo Ul rather than visiting for ourselves, we are transported back via the magic mirror at the end, and there is talk of the Exarch using his spell to summon us again when we are needed. In 5.3 we again use the mirror to return to the Source, and Ryne mentions the tower becoming a symbol of our link to their world, suggesting we continue to have to travel through it rather than simply warping in.