I have just finished training as a paediatric registrar. One of the most frustrating aspects of working in a&e was that the only thinking, calculating, prescribing and documenting desk space was opposite the waiting room.
Endless glares from people waiting and so many interruptions to concentration about "how long". People coming with an "emergency" one minute and then getting frustrated once bedtime approaches and they suddenly want to go home.
The chit chat was not ideal but whilst waiting for systems to load/switch patients etc we are tempted to be sociable and it helps to bond that night's team so that if you are later resuscitating a cardiac arrested child you all work well together and can support each other in the aftermath.
GPs can see children quickly as they should see low risk children and a few questions, quick listen and shine of a torch is enough to Exclude the RARE SERIOUS cases for further assessment. Well until proven sick.
Hospital doctors are trained to work with the seriously ill. This requires a full detailed history and full examination and period of observation to exclude what should be the RARE CASE of a WELL patient who can be discharged. Sick until proven well.
Only nowadays well people come to a&e too (either by choice or 111) and get frustrated with us when we are being thorough or for Making preposterous suggestions to wake a sleeping toddler to assess their "emergency".
As a paeds reg, if someone has referred a child in I am duty bound to exclude sepsis before discharge (or could risk a dead child or a prison sentence for manslaughter as per recent case). We are observing your child's behaviour and observations over time not "doing nothing".
Fevers come and go with illnesses serious or mild. It is not the number of the temp that matters it is the underlying cause or abnormal heart rate etc that cause worry. It is harder to disprove illness and takes time. If the illness only started 2 hrs ago there might not be a red ear to blame yet. If every toddler with a fever of 40 went to hospital the system would collapse. Gps are a very effective filter but are not being used.
I hope that explains a bit why you wait. You should not go to a&e with an illness mild enough that you expect discharge. You will get a better more appropriate service from your gp.
Also remember you don't know what we have just done. I have gone to A&e straight from seeing very preterm babies and doing emergency airway procedures, children dying from a brain tumour, unsuccessful resuscitation of a child whose head was run over by a neighbours car and from telling parents their child has cancer. Getting an earful because Ryan has been waiting 3 hr with his earache takes the biscuit. We try to be poker faced but are still human.