I also had in mind those variations, I was thinking about Jason's b122 when I mentioned advancing strings.
He can use a lot of d4s of course, the thing is it does not really pay off as in the other variations. You hit him with a d4 in fisti, ok. Then what? Cage safe options after this are retreat or follow up with a f3 which leads to nothing. Jason has nothing to fear about Fisti Cage d4 in terms of damage.
Furthermore, fisticuffs only source of real damage is f2, that's the only point here in using d4, forcing the enemy to crouch. The low option is there, in the 113, but everything that comboes after is very unsafe on block (besides the exforceball which does shitty damage and also there's the gap after 113...).
I'm not saying Fisticuffs is worse than any of Jason's trash variations (to say that we should look at every other matchup in the game with them). But in my view FC Cage does not have advantage vs any of them.