That's a good point. While there are other ways of propulsion inside the atmosphere of a planet, it makes most sense for a Nautiloid to use helms for that. BG3 is also set some 120 years after 2e, so everything we see could simply be technological and magical progress.
I should probably add that helmspeople aren't permanently drained, but only lose their currently memorised spells and can't use psionic powers, etc. It also works with spell-like abilities. I guess this, along with long travelling times, is probably supposed to save dungeon masters from players going world-hopping (although that's a fun campaign on its own). Upon arrival, the crew and passengers would definitely need what's called a long rest these days. For Illthids, it makes the most sense that they use dominated captives.
Astral Space in 2e was a bit like quantum space in the sense that timespace doesn't exist unless introduced. The depictions in BG3 work because all the activities we see need time and space to play out, but once they have, there is no when and where in astral space. That's why you can step through a portal and instantly arrive at the target location instead of travelling through a long hyper tube, worm hole or warp tunnel. All of this goes through astral space without people ever seeing it. The WotC version kind of combines the astral plane and Phlogiston.