You don't, but your GP does, my mum had a fall a few months ago, the GP said they suspected a hairline fracture in the hand. This was not an emergency, it was 3 days after the event.
However the GP has no facility to send someone for a quick sit and wait X ray (they used to be able to) so we had to do 11 long hours in A&E
It could be so much more efficient, there are 3 streams of people, those who clearly need emergency attention, those with urgent minor injuries, and those who are clearly just there because they are concerned, particularly mums with small kids.
But everyone has to wait for the same triage, hence forming a bottle neck - if the minor injuries could go and sit and wait for a nurse to manage them in one place, and those with concerns could quite quickly see a doctor, the main unit could process the bigger issues quicker.
And the idiots who have clearly drunk themselves to oblivion should get a bill for the service.