I don't know. I find it useful in practice. Apart from anything else it means there's (probably) no point looking for an exact polynomial-time algorithm, which can save a lot of wasted effort. But it also gives useful clues about what sort of algorithmic approaches might be useful, and allows you to relate your problem to a huge amount of existing research.

It's really basic taxonomy: what sort of problem are we dealing with? If you don't know that, how could you even begin to design a reasonable algorithm for it?