I never play with a shoulder rest. I never have. It is simply the way I taught myself to play, and I find that it has many tonal advantages because of the freedom of movement that it affords.
It dawned on me, however, in a sectional rehearsal the other night with a bunch of viola-playing kids who use shoulder rests, that it is certainly possible to lift the instrument to meet the bow while "wearing" a shoulder rest. The problem that I find is that a lot of younger players who use shoulder rests simply don't do it. They rely on the shoulder rest to hold the instrument up, and they make their sounds by applying their fingers and bows to objects that are almost stationary. This allows for a certain amount of control, I suppose, and it also allows, so I've been told, for a certain amount of physical relaxation, but for my musical purposes there is an awful lot more that I want to do when I play than relax and be in control (though being comfortable and having a reliable technique are both essential).
I find the process of making sound by applying the bow to an unmoving instrument is kind of like having one hand clap while the other one stays still (try it, and see how expressively you can clap). I find that using the energy of both arms (and hands) to allow sound to come out of the violin or the viola opens up a lot of expressive possibilities. It increases the size and depth of the sound, makes playing a lot easier, and can even be done with a shoulder rest attached to the instrument.