They'd need to pay somebody a significantly higher salary to be in charge - somebody with DSL training/a senior member of staff. Probably somebody to train school leavers as they're the most likely to be available at that time of day.
There's paying site staff to stay later.
It's not standard educational activity. There would need to be ways of keeping kids and parents away from the majority of the school premises. Somebody controlling the gate when the office staff have finished for the day. Working around parents' evenings, open evenings, parts used as polling stations, INSET days.
Depending upon the school itself (maintained or academy), the financial procedures could require it to be run as a separate entity, at which point the law requires them to not provide use for free or at a reduced cost.
Separate insurance. Variations to contracts and the associated increase in employer's contributions.
The implications for somebody expected to do breakfast club, lunch cover and after school on their maximum working periods, especially if they're also working throughout lesson time, as they would then require mandatory breaks, taking them away from children in school hours.
Separate accounting for the ASC, increasing the cost of finance staff, bank account administration, different legal requirements.
Credit control - as parents can and do omit to pay and then don't turn up to collect their children, thinking 'it's just the school, they're already there, why should I pay for this?'.
And if nobody wants to work 11 hour days with no break for a fraction over minimum wage, they're in the same position of having to close the ASC if they can't find random teenagers prepared to be there just when older women would need to look after their own children.
Add in holiday clubs with a whole other world of issues on top.
It's very complex and fraught with difficulties - which is why it's been something that external providers do.