But schools are still subject to normal legislation - Health and Safety At Work, COSHH, health and safety of pupils. You can't just forget that because it's inconvenient.
You don't need to forget that. Health and safety at work is not going to state that schools can't have hand sanitiser at the moment. If it does state that it will be changed.
So, yes, hand sanitizer overcomes some of the practicalities of no access to hand washing facilities but does bring its own difficulties, which also have to be mitigated. So, I'd imagine you need lockable dispensers for the hand gel,to stop bottles from being stolen.
Yes, there will be difficulties which will have to be mitigated. This has happened in every other workplace (not just with sanitiser) and schools will be no different. Things are not ideal but that doesn't mean the problems are insurmountable.