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This logic appears specious. Many NP-Hard problems are simple to state.
Kolmogorov complexity doesn't care about time-to-solution, just length of minimal description. Logical depth incorporates time-to-solution.
If we don't care about the time to find a good solution, then maybe? For many problems there is a naive solution (brute force) that is trivial to describe and then there are better algorithms that are harder to describe. E.g. most combinatorial problems, matrix multiplication
1/ Fermat's last theorem is an counter example. Unless you are claiming that there is much simpler solution. Millennium problems are in
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