I work in a similar area that does work a bit like you describe.
The referral is triaged and you are allocated to a pathway with a set waiting time - 4 week wait, 8 week wait, 16 week wait, say.
Then the waiting list is sorted by date of the end of your waiting time.
So more urgent cases do go ahead of others that are already on there.
It works very well when there are enough staff.
But once people start missing their appointment-due date because we physically can’t offer enough appointments, it snowballs quickly, and the waiting-time limit gets pretty meaningless.
It will show that nearly everyone on the list should already have had their appointment, but they haven’t.
It will show that a highly urgent case referred now ought to be seen by mid October. But they won’t be because the highly urgent cases from May are still waiting, and so are the urgent cases from March, and the routine cases from last December.
Once they’ve been on there a while, they really need to be retriaged anyway - but that takes up extra time too.
Throwing more staff at the problem doesn’t necessarily help, if you need a room to carry out appointments, and there isn’t an extra one available.
Or you need a specific assessment and there aren’t enough to go round.
Once you lose control of the waiting list, it’s really, really difficult and really, really expensive to get control again, and that’s what we’re dealing with now, across all services.