I always thought "NP-complete/NP-hard" metaphor only meaningful in theoretical work. In practice, it does not make much sense in guiding what/how the real world problem is to be solved.
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?
Maybe you are heavily on huge algorithmic work. In practice, most algorithms are polynomial-time, and we are looking for under-polynomial-time alternative - log(n). For exponential-time, we are just looking for an approximate alternative.
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?