I agree about Spassky (iirc following the 1966 WC Match Petrosian-Spassky, Botvinnik beat him as Black in the same main line variation, in that same year!). Also one could argue that Tal was not that successful against the Caro in his WC Matches. In 1960, he scored rather well, but as he mentions himself somewhere in his book for the match, he objectively got a good position out of the opening in 1 out of 6 games (caveat: use the above statistics & comments with a grain of salt as I reproduced them from memory).
But my feeling is that Tal & Spassky were nevertheless sort of pioneers in trying out the attacking systems they chose against the Caro (Shirov also comes to mind). At least they pushed their opponents to the limits in these WC matches.
Now back on Fischer: well after a certain point Fischer was like a machine, I think he could overcome any resistance. But again my feeling is that the C-K posed him more difficulties than say the RL (for the White side of the RL or the Sozin, I would certainly say he was at a league of his own).
But I understand your point of view and respect it. In essence I have found Tal or Short more inspirational for the White side of the Caro and Fischer who is my favourite player much less.. Maybe that is contrary to statistics, but is still how I feel.
Maybe if Petrosian had tried the C-K in the Candidates 1971 we would have had a definite answer. I don't think Fischer would have tried the exchange var. again and also Petrosian the fianchetto defence experiments vs. the Panov-Botvinnik.