It's a valid concern to be sure, and one with a lot of interesting historical background. Foundations of quantum mechanics was a taboo subject in physics ever since the Bohr-Einstein debates, and still is to this day, in some circles.
And mosts physicists actually do this; they don't worry about intepretation of quantum mechanics in their work. They use the Schrödinger equation and the Born rule for their calculations and leave it at that. This is often referred to as "shut up and calculate".
But the measurement problem, addressed through these interpretations is a foundational problem, and the tricky thing with those is you have no idea what the implications might be on other foundational problems. An understanding of the measurement problem may very well have something to say about other open questions like the arrow of time or quantum gravity. It could even have implications for the scalability of quantum computers.
And I don't think it's fair to say that this question is empirically unanswerable. A number of possible interpretations have actually been ruled out by the bell inequality, for instance. And both theoretical and empirical research on this topic has seen a resurgence in recent decades.
On a purely sociological basis I feel inclined to think that the reason the measurement problem has seemed so incalcitrant is not because it's fundamentally unsolvable, but because physics as a field has denied itself from actually trying to solve it, and actively pushed out those who dared work on it.