Mikey, steam and grooming will always rectify a nylon carpet with this problem. Wool mostly, although if the carpet has had a lot of usage, and the pile has started packing down in the wrong direction (not unlike shading) it can be difficult to rectify the wool pile.
Scott, thanks for the description.
Billy, the cardboard tube is responsible for a lot of bands at the start (inside) of the roll. It can be as you say, the tube flattening, and also the edge (or the start) of the carpet can set up some bands. Rolls stacked on top of each other is the main culprit. And pre cut and stored house lots are often a problem, because most don't have a cardboard core, and often get flattened before they get laid. And a loose roll can have the sides squashed, and also end up with crush bands.
Steven and Josh, your terminology is correct. The carpet manufacturers here call it roll pile crush bands. I got tired of typing all that and just call them crush bands.
With the popularity?!

of polyprop, I'd like to find a way to fix these, if there is a fix.
M