re: Why don't they put the foam on the inside?
I've looked at designs like that, particularly for hydrogen. Liquid oxygen is not something you want in contact with almost all foam formulations.
Also, if you lose a chunk, it heads down for your outlet or engines. There are damn few things, if any, that will float on liquid hydrogen.
More trouble than it's worth.
The best thing is to design systems that aren't that damn fragile, or where the fragile parts are above the propellant tanks. On a Saturn launch, chunks of ice rained down that looked like they could flatten a car. They bounced off the robust structures at the bottom of the stack, and the fragile payload was up at the top.