This exists in almost every company by design. Engineering teams wouldn't make any progress towards their mission if they are constantly dealing with outside interruptions, but at the same time there are things which should be qualified.
Customer support is a cost center and the focus is on mitigating the cost of providing that support. If you fail to do this you can burn through a lot of cash quickly. What management needs to realize is that this is also an important interface point which requires attention. This doesn't happen at all, or is inconsistent.
It's important for at least the following to happen:
1. Bad issues that engineering will fix don't get stuck in support.
2. Product management review and respond to feature requests, or enable support to respond to customers.
3. Support have a reasonable level of technical and communication skill, and are empowered to answer for the company.
4. The organization works through rather than around support.
What I've always found interesting, is that all of these are often failing in some way at the same time in an organization of any size.
Your role as the back channel is helping to provide some coherence here. However, things can go bad if you left. Inevitably, this is the fault of the company, but when I've found myself in this position I've tried to "promote" people in support to take the lead on this role. Further, formalizing the special request process to be minimally tracked helps visibility with my manager and others. Eventually managers ask why you have become a gopher.
Improving the workflow often involves helping support build relationships with engineering. Management can buy in if support attrition is high (it often is if there is a limited career ladder for support) and it can also improve their perception when people are focused on trimming support cost.