If you think the problem can only be solved by management attention, and you cannot demonstrate to your management that the problem is impactful enough that it deserves their attention, either you are incapable of making a clear enough argument to focus on the right problem, or the problem isn't actually as dire as you think it is (or management is bad and wrong, or at the very least mismatches your values).
Two of these are a signal that perhaps you shouldn't be promoted. The third is a signal that you should leave.
In a less generic sense, I think that there are almost always ways to improve incentive structures and encourage people to focus on specific problems that don't directly involve SVPs. Your manager has some control over your rating. If you can argue that "customer happiness" should be a priority and as part of that, end to end bug triage time will impact ratings, you have successfully created an incentive structure that will reward that, without involving anyone who can modify compensation structure.
