Well, first Donald Trump has to get into a position where he can actually ask Japan to do that. Second, you do realize that the Japanese "Self-Defense Forces" are one of the top ten military forces in the world, don't you? It's not like Japan is only armed with peace signs and Hello Kitty. They've got tanks and helicopters and satellites and everything you need for defense.
The US has reasons for protecting Japan and that's not limited to the use of military bases on Japanese islands.
I expect that Mr. Trump will discover that there are some pretty good business reasons for business as usual. The collapse of Japan would have significant consequences for the US economy. Plus, if Japan decided to kick out the US military (many Japanese would be quite happy not to have US bases in Japan), the US would have to find different options that might not be as friendly or as cheap.
Asking Japan to pay for US military protection would probably make Mr. Abe quite happy. He and many members of his party have been trying to weaken the peace constitution ever since . . . well, for decades, really. They'd just love to say to voters, "Look, we can't depend on the US. We should strike this clause and get to work building our own military." I don't think many Japanese realize they have one of the top ten militaries in the world, either. I think the voters would give Abe's party a blank check if the US started making a fuss.