I think you are just redefining things, the problem still exists
in your example, you seem to have a problem that you can't solve, but the problem itself is solvable ( just not by you )
its like having the problem 2+2 = ??
and you can't solve it, so you say, pffff, math is inconvenient. The problem still exists, and has a solution, but its just you have decided not to care about it / reclassify it.
Now this is different from a problem that provably has no solution. Like "the halting problem" and leads into Gödel's incompleteness theorems. You may regarded it as inconvenience, but in essence it defines a 'limitation' of what one can know.