Castles of Jira Tickets

I've recently taken over some aspects of team management at work, and it's stunning how much duplicate work is done at a large company. At work, there's an internal ticketing system that facilitates communication between teams, and we have an internal rotation for people routinely clean out and triage the tickets. However, given that everyone is consistently busy, and that there is relatively little downside to assigning the ticket to the wrong person, we end up with a system where tickets are assigned into the wilderness. Lost tickets eventually pile up, and team leads as well as other team members have little visibility onto the current work.

At my previous job, we had a similar rotation, except that the person was responsible for actively fixing the bug, rather than just assigning it to someone else. I've only now begun to appreciate that workflow, since a triage where you simply reassign tickets is practically busy work. People do not feel a need to clearly take a look at tickets, nor do they feel bad when tickets are lost, since there's no external feedback loop of where the tickets should have been in the first place.

I'm also unsure if there's a realistic solution, attempting to force people to adopt a rotation where the bugs are actively being fixed requires coordination between three different teams across two different countries, at a company where remote work is not particularly valued. This causes frictoin, especially as developers see particular services/responsibilities as "not their job". Without changing the culture, the current system looks looks to survive into another year.