Imagine I fill a bathtub full of marbles - and I pull a solid semi circle through the marbles. The marbles that flat side moves past will barely have to move, the marbles that are displaced by the round side will have to 'move further'. They won't come out exactly at the same time, but they will have had to move further and move faster as the semi circle moves through the bath.

This is a great example, and the first time I've heard it phrased this way. Thank you, I'll file this away for later.

How different is this when the "marbles" are compressible?

I guess you could do the same thought experiment with foam/sponge balls in a bath - no matter if they squeeze, they will still be moved out the way and follow the path of the semi-circle shape.