Why would the government want to keep you from doing something that would reduce the load on the medical system and cost them nothing?
Power, that’s why.
They want the money, the government believes that ALL money belongs to them, and they want it. In their opinion the money you pay to a foreign doctor or hospital is not YOURS, it is theirs and you ARE costing them, and they can reduce the load on the system by simply denying you care, (remember those Death Panels?).