In both companies I've been using that, it was a very simple RT/JIRA-SD-style system: "open a subject/text ticket, clock starts ticking, on call engineer gets a non-wake-up memo and will reply with high priority during work hours" and ticket will get closed ASAP and we do achieve inbox 0 regularly.
Yes, there are obvious issues and it requires two things to work:
1) If you actually have no clue about the product, you are respectfully told to fuck off to normal user support channel
2) If you keep misusing this for user support / slack channel, you get your access revoked.
...which are hard sells in large companies, of course—on the other hand, in BigCo I got success in getting an engineering headcount to accommodate that.
How do you propose that queue is prioritised and consumed by the development team?