One should always wear ear protection when driving bridge pins whether the board is wedged or not. In terms of creating a less flexible platform there's no reason you can't wedge the board down rather than up. The non linear spring quality means that the assembly will stiffen as you wedge it down.
One place where I think it is important to insert wedges, whether you wedge the entire board or not (I don't), is between the bass cantilever (if there is one) and the panel. You don't want to drive these wedges too much as you will be possibly stressing the bridge/panel glue joint. That means you might have to tap them back into place periodically as driving pins in that section will tend to work the wedges out.
My experience with driving in tuning pins and bridge pins is the best way it to to support the pin block or the sound board directly to a concrete floor. I use an old back post of a deceased piano, and a piece of leather. You have to move the support a few times.Not only the sound board can flex, the whole body of the piano can flex, even the casters.You feel the difference in your hammer.