What is deficient about the original explanation that the wave function is not real but rather a scientific theory? The issue has been unresolved for about a century now, it's relatively unsatisfying but hasn't held the science back in any way.
Maybe we will even eventually find the ultimate model, a model that describes every aspect of the world perfectly, even though it is not obviously clear how we would determine that we did not miss some aspect of the universe in our models. But even then the map would not be the territory, the model would not be the universe or a piece of it. Imagine a wave function would perfectly describe an electron, would we be justified to say that an electron is a wave function? No, because for them to be the same thing, it is not sufficient that the wave function has all the properties of the electron, it would also have to have only the properties of the electron. But the wave function is an equation, I can write it down or square it, things I can most certainly not do with the electron.
So the wave function is of course only a mathematical description of a quantum system and not a real thing out there in the universe. But that is not the problem, the problem is that we have two seemingly contradictory descriptions of quantum systems. We have the Schrödinger equation describing the unitary evolution of isolated quantum systems and it works really well. But we also have the Born rule and the collapse postulate which tell us the probability distribution of measurement outcomes and how measurement changes the state into the measured Eigenstate, a non-unitary change, and this also works really well. But there is the problem, on the one hand a measurement - whatever that exactly is - seems to change the state non-unitarily but on the other hand a quantum system together with a measurement device is just a bigger quantum system and should therefore evolve unitarily. Something has to give.
As you say, that is very unsatisfying, but it was also not a complete roadblock, shut up and calculate worked pretty well. But I would not confidently declare that this does not hold us back at all, who knows what progress can be unlocked by solving the issue? It might of course also be mostly inconsequential but I guess that is something we will only find out after the fact.
[1] Or fluids if you want to be pedantic.
In terms of what we may/not be missing out on, I say that because it seems few of the possibilities remaining after a century of investigation (many worlds, relational/information based approaches, etc) contain any new physics or scientific insight.
Eg if we could somehow tell that MW or pilot wave theory is "correct", we would still have nothing to do but shut up and calculate the same things, no?
If unitary evolution continues in some sense, we would still need to throw factors away in order for the theory to remain predictive to us.
Particles are only observed to be in a single place at a single time. My understanding is that it may be that we lose the perspective necessary to see them elsewhere, since we are embedded in the same eigenstate (or something close to it). But the task of science is confined to observables. I question, what are the scientific questions that collapse postulate holds back from being solved?