Outright purchase has worked pretty well throughout the history of publishing. So renting would have to offer enough of an improvement over that model to make it worthwhile.
I might be ok with renting a book if more of the money went to the author. Theoretically it could work out well for everyone. A lot of cookbooks would be a great option. Rent them for a month or do for, say, $1? Cheaper access to books for a period of time, like O'Reilly's Safari for technical books.
But I don't think that's how it's going to work out if renting is the only way to get books. I think that everyone will for forced into onerous terms of the publishers get too much power.