Yes I currently have and have had basses with this feature. Current bass is a Fender Jazz Deluxe. No, I do not use the strings through the body. Here is why.
On several previous basses, there was no effect whatsoever on sustain, tone, body resonance or anything related to sound. Also, string life is substantially shorter.
This last point got me to thinking about the effect of break angle on string life. I played an early Alembic Series I long scale for many years as my only bass. Round wound strings lasted forever on that bass. In their variation of construction methods, Alembic had set the tail piece about three inches away form the bridge. This made the break angle on the bridge very low. Yet that bass had excellent sustain, probably somewhat due to the mass of the bridge. Later on. I was playing an SR5 with the string through ferrules and messed with various set ups with that bass. Stringing through always led to shorter string life, no effect on sound.
My theory, FWIW is that the extreme break angle actually damages the core of the string because of the plastic deformation. This causes the microstructure of the steel to become more absorbing of vibrations in the acoustic frequency range at the witness point on the saddle. An optimal bridge design would achieve perfect clamping with zero break angle. Don't ask how that kind of bridge design would be reduced to practice; I haven't figured that out yet.
Meanwhile I never string through the body for the above reasons.