We should always check behind with TT-KK.

Monty, you even said it yourself.

"I fold to anything larger than a 2xmin raise. If he flats it, likely I'm facing a pair of Aces and will not bet again unless I improve on the turn. "

We're not cbetting based on relative hand strength but we're cbetting for a reason. Betting to have better hands call, worse hands fold and always muck to c/raises seems like a bad reason.