In particular, copyright issues would require limiting the number of copies of an ebook taken out over the net at any one time.

But the convenience of taking out an ebook over the net would probably mean that it would be very hard to find highly sought after ebooks since they will always be taken out.

In other words, most people who don't aggressively seek out highly sought out ebooks will never get to take one out.

It seems to me that the public library model really does depend on the inconvenience of going to the library and carrying physical books.

Update:

There's also the issue that many people today go to the library without a specific book in mind and just take out books that they find by chance. In an ebook library, I suspect that everyone would be searching or browsing hot/top lists, thus making it very hard to find a good ebook that is available without a long waiting list.

In other words, not only do public libraries depend on the inconvenience of going to the library and carrying physical books, but also on the inconvenience of finding books that you would like to read.