Indeed NP problems are in a way astonishingly easy in that they have the very specific, curious property of being polynomial-time verifiable, which is clearly n

Indeed NP problems are in a way astonishingly easy in that they have the very specific, curious property of being polynomial-time verifiable, which is clearly not true for arbitrary hard problems. In other words, problems in NP are those that can be brute-forced because checking an individual answer candidate is cheap. (This is, of course, just another way to phrase the definition of NP: the class of problems solvable in polynomial time on a non-deterministic TM.)