The lollypop is a STOP sign!
Having worked as a civvie for a UK police force on the Road Traffic Collisions section, and having dealt with the paperwork on a few incidents of lollypop-person abuse, I actually agree with this idea.
I've dealt with instances of lollypoppers being driven around whilst kids are on the crossing, threats and actual physical violence against lollypoppers and even one run over by a bus!
The primary problem we had when trying to warn/prosecute such instances is witnesses. You will usually get a few mums, dads, etc come forward to support the loppypopper but as the alleged offender is more often than not someone on the school run, and/or local and known to them, they often don't want to go ahead with a formal statement and hence cannot be used as a witness for a formal warning or potential prosecution.
I do also agree that some lollypoppers can be a bit over-zealous about leaping into the road when they see a kid approaching, and some forces/councils do train and monitor their lollypoppers better than others, so there also needs to be other work done such as more consistent training of lollypoppers and education of motorists that the lollypop is legally a STOP sign.
Usually a formal warning from the police for 'failing to stop...' is sufficient to make people think twice when they realise that that if they get caught at it again it's a hefty fine and points on their licence.
One option we also used to use a lot for minor incidents is a driver safety awareness course. These are usually run by the local council, the driver has to pay a small fee for it, and it can be offered as an alternative to prosecution (some complain about paying for it but when you point out that the alternative is a heavier fine/points they usually see the sense of it).