I agree that it's odd that we have atomized the writings in the scriptures. You can find reader's editions if you want to remove the verses structure.
However, I don't agree that the verses are "diametrically opposed to a Christian reading of the Scriptures". I believe that there is room for both reading whole books and reading short quotes.
For instance, I don't think there's anything wrong with taking John 3:16 out of context because it is a very straightforward verse. It's really nice to be able to share verses easily by giving a <Book> <Chapter>:<Verse>. There is danger though when we do that with all verses of scripture, and we should be careful to study the context for verses before coming to any conclusion.
The key is to actually study the scriptures, and not just take the easy route and find verses that make you feel good about yourself. But that's easier said than done.