good grief what a world we live in. 
yes, my dc did expect a sick child to be collected within 10 mins, certainly no longer than 30 mins.
Unfortunately, many schools don't have sick bays, or indeed anywhere for sick children to go, or anyone to look after them/ school nurse.
Children were being left for up to an hour and the schools round here took action. Nobody expected it to necessarily be the parent though, a gp, friend of family, extended family etc.
There were children standing in the playground chucking up into buckets, not nice for other children in a small playground when they went out to break and more importantly no good for the child who should be tucked up in the warmth.
I'm surprised parents don't accept this, it's quite shocking, tbh.
I used to cover for a couple of dd friend as did other parents who could.
We did emergency contact, inset days, snow days etc.
I know it's hard when you work, but as I say I'm surprised that some parents think it's fine not to have local cover when they work so far away from school.
It obviously must just be me then, maybe it was seeing the distressed children with nobody looking after them.
I would like to ask parents who think local cover is too much to ask for who on earth they expect to look after their ill children, whose job is it and where on earth they expect schools to place ill children, when there is nowhere in the school to do so.