No baggage "with wheels" as carry-on?
You've gotta be kidding! Most of the kids in Grade 1 these days have backpacks with built-in handles and H-frames with wheels at the bottom so they don't have to hoik bags onto their backs that weigh as much as they do!
Most luggage designs that I've seen in luggage shops (you know, the one where you can get the whole matching set from the "makeup case" all the way up to "refrigerator crate" size) specifically design the hand-luggage size bags with the handles and wheels at the bottom.