It is right to be suspicious of formal proof. In most areas of software engineering, employing formal proof makes you about 10-1000 times slower. Knowing how to do a formal proof in principle though lets you often reap a lot of the benefit without actually getting slowed down much. This is similar to how mathematicians know how to prove something in principle without running it through Coq or Isabelle.

By the way, Curry Howard is just one way of doing formal proof (one I personally don't like). There are many foundational and practical problems that need to be solved before formal proof is ready to go mainstream (but I am convinced that it will one day).