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It could work. I made one by reconfiguring a small Quick Clamp (the kind of wood clamp tightened with a pistol grip handle). This one looks like it could be far simpler to build.

The problem is that there is no way to twist the wheel. Especially on Carreras, the knurling is spiraled, so pulling the wheel straight off actually routs a larger hole in the hub. I never got past that feature when I was trying to do this. That, and the first one I did had a bar under it that got in the way of the crown gear and made it a front axle only puller.

Train wheels are locked on the same way a revolver's barrel is locked in the frame of the pistol. The inserted part, in this case, the axle, is frozen and the hub slightly warmed, so when it screws in, the threads are locked by expansion as the barrels warms up.