"no-one can run a plate on a foul ball, yet can still be caught or run out. That just stinks... "

If by run out you mean tagged with the ball and called out, then you can't be. But your foul ball can be caught.

"I just can't see why you're not allowed to run until the ball hits the ground (or is caught). "

You can run, but if it is caught you have to 'tag up' on the base you left or otherwise they could just throw the ball to that base and you're out. so someone can't just hit a high fly into the outfield while the runners advance 2 or 3 bases. now the infield fly rule is a whole different ball game..