SNL hires a lot of people with improv background because that's where comedy makers are. They hire just as many people from stand-up backgrounds, because that's the other place comedians are. Last year's new four were all stand-up, like Pete Davidson.
Improv players are in a good position because being able to create comedy in the moment (improv) is a good proxy for being able to create comedy over a week (SNL). Writing is so important to SNL that players must either write themselves or partner with a writer to get airtime.
Some of the best moments were improvised, for sure, but they're not planning on it (obviously) and they're not depending on it. The sibling comment said enough about that.
> The writers change up the script until the last second, anyway, so the players are usually just as surprised at their lines as anyone.
Yeah, it's written. They're reading the lines. Not improvised. Obviously they're bringing creativity to it in their acting, but they've heard it in pitch meeting, they've contributed to writing it, they've heard it at table read, they've heard it at dress rehearsal, maybe a line on the cue card has changed.
There are moments of improvisation, but SNL is emphatically not improv.