The same dirt comes into the rooms no matter the flooring. The carpet just hides the dirt from your view a little more. but it's still there. I'd rather be able to see it and take care of it than to have it all in the carpet constantly becoming airborne with each vacuuming.
But yes, removing your shoes just inside the door would likely make a big difference. If you're not fond of walking barefoot (I can't, myself, so I get it.) you can bring a pair of flip-flops, slipper,
Crocs, etc. to use as your "indoor shoes" while you are in the room....something that you don't wear outdoors at all.