But player behavior is different in Premier and Quick drafts, in part because of the price difference.
Exactly. Players are more likely to rare draft in Quick draft to build up a collection, while in Premier draft they're more likely to optimize their decks for winrate.
If the bots allowed players in Quick Draft to end up with all of the rares, and every deck you play against contains six or seven rare cards, that wouldn't resemble drafting with other players either.
If they're bad/mediocre rares, sure it would. Obviously, it makes sense to have the bots draft bombs highly. It doesn't make much sense to have them be first picking Pithing Needle or something unless the goal is to pinch us on rares.
The bots still distinguish between good and bad rares. Bad rares get passed often - although still not as often as they do in Premier Draft, because Quick Draft players still place at least some premium on them for collection purposes.