Worra I do agree that sometimes colds are minor and sometimes we are perhaps all capable of being a bit precious about our children and what is an emergency. But just a cold (checked by the lab that it was just a cold - culture grown was rhinovirus) led my husband and I to discuss whether my sone would pull through and the risk of being ventilated overnight (he would have been but we were at a teaching hospital where they can keep a very close eye on things because they can act very quickly rather than have to transfer the children from elsewhere where they act first as they aren't on site).
From the paediatric staff I spoke to that was in fact a very common reason for particularly young children to be admitted and some do still die from just a cold.
I don't sanction basically fit children going to A+E but if in doubt I would always recommend that a child is taken there if there is nowhere else to go (and NHS direct don't have sats monitors)
I would also add that when I broke my arm I was taken to A+E by ambulance, because I was passing out from the pain and speed prevented nerve damage from the frankly horrific fracture. So a broken wrist can be an emergency too. In fact IME of the three times I have gone to A+E by ambulance for myself the broken arm was the biggest emergency in terms of speed of response and long term consequences , the other instances were frightening but not the same. (Ectopic pregnancy, probable placental abruption, and broken arm) I was bluelighted on each occasion.
In all cases I have however been seen within 30 minutes, whether the three for myself or the instances for my husband when he blocked his windpipe or my son (the cold as mentioned above, an apnoea attack, and bronchiolitus twice) and on only one occasion I have been there for me or my son did they breach the 4 hour rule. I have gone in at many times of day and night and in my view it makes little difference to wait time.