Your children also run the risk of getting run over crossing the road .
God forbid, Abducted walking home from school..
4 generations of a family were sitting in their front room watching 'play your cards right' when the Lockerbie aeroplane parts smashed through their house and killed them ...
Are you really going to deny them the simple pleasure of camping with their mates in the garden, midnight feasting with their friends on a birthday , all because of a ridiculously small possibility of 'what if..'
Where does that end ? Will they be allowed to learn to drive ? Take a gap year abroad ? Go to a mixed sex party aged 16 where they could, if they chose, to have sex without your knowledge?
All those activities are incrementally more 'risky' than the chance of attack by a paedophile at a friends sleepover.
It's all risk and all balance . The moment things are 'banned' rather than supervised they become 100x more desirable and before you know it they are exhibiting behaviour far more concerning than the desire for a sleepover as a rebellion against what they regard as peculiar parental behaviour.
Sleepovers are 'a thing' with children from primary school onwards . There is no avoiding the fact. You may not like them but that it is so. If you can't find a moderate compromise you will become known as the 'wierd' parent , which may not concern you one jot but will mortify your children.
Birthday party invites will stop (as you don't do sleepovers they won't get invited) Friendship groups will start to leave your children out because the others are having sleepovers at weekends and in school holidays and your dcs will be out of the loop..
Not too bad now but really really important for secondary school age, where establishing friendship groups is everything.