The actual amount of centrifugal force is also tiny. Sure, it's a relatively fast linear speed compared to something like a merry-go-round, but a merry-go-round's angular velocity is much higher, and that's the one you use when calculating the force trying to fling you off.

Also, centripetal force is the inward force observed by an external non-rotating reference frame which deflects motion into a curve. You've conflated it with centrifugal force, which is the outward "fictitious" force experienced in a rotating reference frame.