> If I defined some pointless construction and it turned out to be very difficult to prove, it would absolutely and automatically over time be considered a "high utility" problem (again, for some odd reason).

Yes and no.

No: There are lots of very hard open problems which are judged to be of little value by mathematicians and hence garner little attention.

Yes: If a conjecture resists proof for a long time, this can indicate that we still have a substantial gap in our understanding. We project utility into an eventual closure of this gap, not into the statement of the concrete conjecture at hand. The gain in understanding is what we actually work for. It just turns out that chasing specific results, even if they are mostly dead ends on their own, is useful for orientation.

The (by now solved) problem by Fermat (for all integers a ≥ 1, b ≥ 1, c ≥ 1, n ≥ 3, the equation aⁿ + bⁿ = cⁿ does not hold) and the (still open) Collatz conjecture are perhaps good illustrations of this situation.