Children can manage unaccompanied flights perfectly well. I did as did most of my friends at boarding school because we all had family homes outside the UK.
However, up to a certain age, and this would have included being 10, we travelled as unaccompanied minors which is a completely different status to that proposed where the parents sit upfront in a different cabin.
I've no doubt that a 10 and 13 year old could cope with travelling alone on a flight to the US. It's whether they ought to be doing so on the basis that one of their parents refuses to tolerate travelling in economy.
Of course, if the children in question think this is a brilliant idea that might be different. But if I discovered I'd innocently acquired the routine looking after of someone else's children because their parents declined to sit with them I'd be a bit po-faced. Because it isn't just the possibility of emergencies is it? It's the general "my video screen isn't working", "we've not got enough pillows", "when are the nuts coming round?" sort of stuff that is just as distracting when it comes from other people's children!