Yes, being more cautious with relatively strong hands, as opposed to universally strong hands, is a good idea.
I was saying yesterday how often a flopped two pair, especially the bottom two pair, ends up getting beat by a counterfeit or better two pair on the turn or river. You have to keep in mind that if the opponent has flopped top pair with a good kicker, they are not likely to fold even if you move all in on the flop to try to get them to go away.
It is a good idea to slow down and take a moment to consider all of the factors in any given hand, at any given moment or street. You are trying to make the best decision, and sometimes the best decision is to fold your two pair or trips.
However, I am not sure folding a set postflop is ever really a great idea. I can see the logic behind folding if the board flops three of a suit, or three straight cards, but you have to remember that a lot of players will likely slow play a flopped nut flush or straight, and often they will lead out when they only have the draw. So I don't see too many spots where you will be put to the test and have to think about folding a set on the flop.
Consider that a flopped set of 10s on a board where your opponent flops the broadway straight is still at 38%
equity when the backdoor flush is in play, and at 34% when it is not. The set is also at 34% equity when the opponent flops a flush. So I think anytime you flop a set and move all in or call an all in from an opponent who flops a straight or flush, you are excused from questioning yourself when you don't hit your quads or full house.
I have folded sets on the river. Only twice that I can remember; once the guy showed me his
bluff, and the other time they showed me the nut flush that my set card hit for them. But I have never, ever folded a set on the flop. I am not sure I ever will either.