With three caves, you'll be getting cards onto your mat three times as quickly, and then scoring three times as many points per card on the mat, so that's 9 times as many points.

That's not true, because Cave is terminal, and decreases handsize. Without villages you can't put away more than one card per turn, and without villages+draw you can't put away more than two per turn.

There is no rule against quadratic payoffs - see Bridge, Goons and Merchant Guild - but notice that for each of them, it's hard to play a lot of them, because they don't give either +actions or +cards. Madman has exponential payoff, but that's OK because it's hard to

*get* a lot of them in the first place.