If it required you to make arguments in the form of First Order Logic statements and then did automated validation of them, then I would use it. I'll grant this is probably a niche use case. With the power of modern automated reasoning, and maybe automated fallacy detection, it seems a shame not to use that. Computer assisted argumentation would be a great forum feature.
That makes no sense in practice. The reasoning you employ on a day to day basis is completely outside the realm of what you propose. Realistic everyday reasoning is too complex; it is not satisfactorily represented by first-order logic.
Also, even mathematical proofs are cumbersome to state in a purely formal way. Moreover, many of our arguments hinge more on things like accuracy of assumptions, informal inferences, disagreement on "axioms" and goals, etc, not on formal validity of arguments.