Some times not knowing the history and hardness of a tasks helps in a novice attempting an impossible task, and arriving at the solution, completely ignorant of the history of the problem.
That's one of best motto I've ever heard!
Second, because the proof won't be useful outside of arcane theory. If P != NP, that verifies something everyone already asumes, so it wouldn't change much except for abstract curiosity of a few experts able to comprehend the complexity of the meaning.
Even if P = NP, prime factorization can be very time consuming to solve. The prime factorization problem is in the NP class, but we don't know if it is NP-hard.
What would be very interesting - and likely give pretty deep insights into the very nature of computation - would be how exactly they proved it.
P vs NP is the same: if solutions to a problem are easy to check, is there always some better way to analyze the mechanics of the checker to make those solutions easy to find, so that we aren't stuck with brute-forcing it? Whether the answer goes one way or the other, the point is that solving the problem would have to provide some insight to the effect of "here is a periodic table of elements for all of the 'easy' algorithms -- and here are the properties of all the 'molecules' made by combining those building blocks." And only once someone advances our understanding with those cutting insights can we say "yes we can always reach into the verification mechanism to understand it well enough to build a better-than-brute-force algorithm" or "no, here is such a thing that algorithms cannot do, it's not just that I am not smart enough to find a way for them to do this -- they are fundamentally incapable of doing it faster."