I don't really see the need for string through either. For starters I always like to unwind a new string right after initially tightening it up and then back it out of the bridge to straighten it out as they inevitably get twisted. To me, doing this is the most important thing to making a B string sound good and it's almost impossible to do when it's strung through the body.
I never understood how the through bridge bridges would lift considering how there's a massive toe that is countersunk into the body which you would thing would counteract any pull from the other direction.
I do the same thing and I agree completely. Alot of time on my basses with string thru body bridges I will run the B String through the bridge just so I can do this.