I don't get your P = NP example. If P = NP, it has serious consequences. E.g., as I understand it, a lot of cryptography will ultimately fail if we discover that P = NP.

We have no reason to believe that P = NP, but on the other hand, without proof, we can't know for certain that it doesn't. We're not infinitely smart, and we just might not have yet seen the way in which P does equal NP.

Surely we live in a world filled with uncertainty, and we have to be able to deal with that. But in instances in which we can be certain about certain things, it certainly benefits us.

Also, I don't understand the argument that learning to think with the rigor of mathematics is somehow detrimental. There are many different ways of reasoning, and a well-educated person should strive to learn a good amount of these useful mental tools. Learning to think with mathematical rigor is a good tool to have in one's mental toolbox.