This idea of the crew or parts of it returning after some days doesn't make much sense if you consider that if there was a crash there would be a search and rescue operation right away.
I guess the idea was that it was you who has to execute CSAR. Which you might not be able to do right away. So if enemy doesn't arrive, and friendlies don't arrive, survivors hitchhike out and you lose whatever equipment survived the crash.
It all depends on the setting. I agree this all doesn't make much sense in vanilla setting. There are others though.
Also, why would aliens be present on a crashed xcom craft site?
They don't, unless they come, as you say. They might not be able or willing to come though.
The aliens could assault the crashed craft right away (and you'd be defending it, so essentially another ufo mission), but it doesn't make much sense for these sites to be present for days or weeks.
The first part I agree, but still think that for some settings having to do SAR yourself or lose stuff and possibly more people might make sense.
I'm of no opinion on whether or how exactly to implement this. Got to do the basics first. Let's return to this after hostile intercepts and multifights actually work.