If mathematicians behaved simply as you describe, then those resultant extension theories would never have been developed, because everyone would have applied modus tollens regarding in a not-yet-proven-useful case. (Disclaimer: I know nothing about the actual historical reasons for the first explorations of complex numbers.)

Therefore, it's best for mathematicians to always keep the M-T and M-P cases in mind when using a proof by contradiction. Of course, a lot of time the contradiction arises due to theorems already proven from axioms, and what happens if any one of the axioms in a theory is removed is usually well explored.