If your opponent is very likely to bet vs missed cbet with all his crap, yes, it's better to c/r some gutshot, overs and whatever hands have some equity which you would have cbet and shut down.
It's actually easy to have a strong enough range to do it with: add some NFDs, some OESD with overs and maybe some overpairs on low dry board. On very wet boards, if opponent likes betting and spewing you can include sets ofc. Against a bet/fold happy opponent you could literally replace cbetting OOP with c/r flop since he bets all crap and you raise what you would've cbet but have more money to take from the pot now.
Yes, it's an unusual play to do nowadays. Think about it: your goal is to get people out of their comfort zone since they are more likely to make mistakes. What do they face often? Cbets! They are comfortable playing vs cbets. When you check as pfr it's usually a whole new territory for them.
Like I mentioned before: cbet and give up doesn't cut it that much nowadays. You need either to put pressure on future streets or play flop another way.