What if I build a low, heavy, wheeled table about 24" high or thereabouts,
such that I would always have to sit down to use the thing.

Not a good idea, in my opinion. The idea of sitting and turning is
attractive but doesn't really allow you to use the tools properly. I learned
to start the tool cutting and then move my whole body in the direction of
the cut. Difficult to do when seated. In Dell Stubbs video, Bowl Turning, he
talks about the dance. Later in the video you can see him moving around the
lathe almost like a dancer as he makes his cuts. It seems to work for him
and there is no way that I'd argue turning with him!

Just my two cents,

Harry