Checking bags adds a lot of time to your trip after the plane lands, you have to wait ages in many cases for the ground crews to unload and process your baggage. In addition the size for carry-on luggage is pretty large with a small amount of work you can pretty easily get all you need for a trip into the carry-on baggage.
Except for a few bad days, I generally don't wait long for my checked luggage. It's sometimes already there by the time I make it to the claim area. Finding overhead space can be a hassle and I much prefer boarding and unboarding without dragging a ton of stuff. And carry-on obviously limits the items you can bring along on a plane.
Your arguments are perfectly valid for some, but this is isn't a case of "this method is obviously right".
The size is basically the same everywhere because there's limited difference in the planes. EG American Airlines which I just flew has the limit of 56 x 36 x 23 cm. Big enough for a one week duffel easily.