The problem with that is that many passages could have several interpretations, and by default the average Bible reader will tend interpret things the same way his/her parents or pastors or friend or favorite musician or the writers of The Simpsons interpreted them.
By trying to avoid modern bias, one ends up with whatever assumptions are so ingrained in popular culture that one wouldn't even think to question them.
One use of reading modern books (and not-so-modern books) about the Bible is that it's a way of being exposed to those other alternatives, so a Bible reader can make a conscious decision about what they think some passage means, rather than reading something between the lines that might or might not be there and not being aware that they're doing it.
I think CS Lewis's recommendation to alternate between new and old books is a good one.