I don't know if I agree with your definition of a c-bet. I was under the impression a c-bet is simply making a bet after having previously been the raiser in the preceding round, i.e. I'm the aggressor.
It is IMO not designed to make your opponent fold when you believe your hand is not best. If I have AA I raise and then follow with a bet. I still consider that to be defined as a c-bet and I rarely believe my hand is not good post flop when I hold AA. Say I raise with JJ pflop and hit a J on the flop. I will still many times bet the flop. I don't think my hand is second best as I bet out and I still define it as a c-bet. So I guess I don't agree that a c-bet is designed to make an opponent fold. I see a c-bet as being designed to get your opponent to make a mistake, to call with improper odds
or a worse hand.
Alternately as you stated the c-bet helps you find where you are in the hand.