Naturally, as if you are able to deprioritize something long enough it shouldn't be done.

That's good. A lot of people will come to you with ultimately low business value asks. It's just how it is. People have ideas, they want to briefly discuss it, I direct it to the backlog. If the EM and the Product Owner both consider it low-value, the requestor has to accept that fate or create a more compelling argument for why the assessment was incorrect. But most requestors won't put in the work to justifying the requests. There is no problem with backlogs becoming graveyards. We might revisit the item later if business priorities change yet again, and now we have a paper trail of the decisions.

If the backlog keeps growing either the tickets aren't important or you need to grow your capacity through additional headcount or vendors. As a manager it's your job to communicate the implications of both.

If they never outrank new requests then yes. If you're backlog grows and grows consistently then that's a signal to hire more people.