Where I live you can walk into a shop, buy a smart phone, then pop in a sim card and be off. Can you not do this in the US?
You don't pay any monthly service and I don't see how the carrier you have chosen to buy a sim card from has any basis for claiming that the phone I'm using is somehow not owned by me.
Since I purchased my first mobile phone around ~11 years ago this is how I have always done it.