The Goldbach conjecture is of very little interest to mathematicians, unlike either Fermat's Last Theorem or the Riemann Hypothesis. Statistically it is clearly true, in the sense that there are way more prime numbers than you would need for it to be true. Finding a counterexample would be interesting in the sense that it would be very surprising (but not mathematically interesting).

It is fated to be proved as a trivial corollary to some more important mathematics; a corollary that no one would have bothered with if not for the historical importance.

The unsolved Twin Prime Conjecture, of roughly the same age, is expected to lead to much more interesting mathematics if it is proved.