You will most likely have some dispute from people citing special needs, etc. Outside of North America it is more common to have those smaller wheeled trolleys for use airside.

I mentioned my carry on luggage a few posts ago, and neither piece has wheels. I only use one arm much of the time and I do manage just fine carrying and lifting my bag(s), and don't seek (or expect) assistance.

I can see how in certain instances a ban on wheeled luggage would create issues for people, however.