I could see a bookstore managing to pull off a "cover charge"/minimum purchase requirement--if it offered something other than books. A coffee shop, perhaps, with the ability to browse, buy, read and discuss books in the store. Regular book club meetups. Author signings where the author gets a cut of the cover charge. And so on.
It'd take a drastic reconsideration of the whole business model, though; "place people pay to enter" is very different from "place people go to buy things." Even if the entry fee is small, it serves to keep out casual browsers.
$2 per person? $1? Is the entry fee one-time-only or does it last for the day--can you browse, go next door to have lunch, and return? If you buy something, do you get a coupon for free entry next time? How about children? Are they free or do they wait outside while parents shop?
I can imagine a successful business based on it, but it'd be more a "book club" than a "book store."