It depends on what you mean by "correct". If it means "it does what I need it to do and I can move on with my life", then no, the cognitive load doesn't already exist, and formalized type theory in many cases adds an incredible amount of cognitive load.

I know that in many cases "correct" means a lot more than that, such as in proper software engineering contexts when building a program/system that needs to live and evolve for a long time among many people. I write that kind of software all the time, and I always use static type systems for it.

But I also write a bunch of ad-hoc, one-time-use programs, and I'm very glad that I don't need to reason about abstract type theory in order to parse a CSV file and add up some columns to send to a colleague.