On the contrary, failing to feel common sense is usually a sign that you don't really understand what's going on. Your understanding of an abstract concept is only as good as that of your best example. The abstract method in mathematics is just a way of taking features common to several examples and formulating a theory that can be applied in many cases. With that said, it is a useful skill in math to be able to play the game and proceed formally.

There's an anecdote about a famous math professor who had to teach a class. The first time, the students didn't understand. A year later, he taught it again. Learning from experience, he made it simpler. The students still didn't understand. When he taught it a third time, he made it simple enough that even he finally understood it.

I will concede that in practice it can be expedient to trust the experts with the complications and use ready-made formulas.