>>12but if you don't know whether a problem X is NP-hard, literally the easiest way to prove it is by assuming you have an oracle that solves it in P and check if it allows you to solve an NP-hard problem in P. if it does, X is NP-hard. and proving that X is NP-hard has its practical uses, i.e. in designing public-key encryption schemes.
also, science doesn't have to be directly applicable in practice to be useful. the fact that pi is irrational also doesn't affect your life, but it is a basis of other things in mathematics which in turn are a basis of other things in physics, engineering etc. and those things do affect your life.