I have no problem with paying for services including browsing for books. When I lived in the U.S. I would have paid an annual membership to be a "member" of The Tattered Cover Bookstore in Denver and in the local bookstore, The Stone Lion. I realize some understand that all services and products must be paid for but not by them.
Whether it would be a good business plan or not, I'm not sure. Depends on the management, I think. I can imagine a local bookstore, with rooms for book clubs of members to meet, hosting authors for talks and signing books, hosting creative writing classes, and other services might be able to have a members bookstore with occasional browsers paying.
When I was in a book club we would deliver our list of books to the local bookstore and they would order all the books, bundle them, and sell them to our members at a discount. That's a service I value.