I was a bit
about this when I read it, but to be honest I can't think of a good reason not to if the children are happy about it. I do agree the OPs dh is the one that seems a bit precious, but everyone is different and if he's very tall and/or gets more achy than others in a confined space for several hours then who are we to judge.
Can't understand why others are saying they'd be outraged if they were next to unaccompanied youngsters on a flight - whenever you fly it's a lottery who you sit next to and nothing that people can or should complain about (unless there's unreasonable behaviour in which case the flight attendants will sort it). I'd rather be sat next to a youngster myself than a lot of adults (especially ones with BO) and these youngsters sound as though they'll be well behaved in any case. It's no different to finding yourself next to UMs of the same age.
The youngsters themselves will probably love it - if they do mind, then that's the only legitimate reason I can see for not doing it as long as it's within airline rules (which it is for BA at least).
The safety arguments are flimsy. Planes are about the safest form of transport there is, but we wouldn't hesitate to let them use buses or trains unaccompanied at that age or cross busy roads walking to school. Most children are probably more likely to obey the seatbelt rules in the case of turbulence than many adults and in the very unlikely event of something more serious occurring you're probably done for whoever you are sat with.
If it enables the OPs family to have the holiday they want then why not? Life is about compromise.