“the difference between playing with matches and being mechalel shabbos is this:
Playing with matches is a sakanah to the kid’s life and has to be stopped immediately.”
Being mechalel Shabbos is a sakanah to the kid’s spiritual life — which is much more important than his physical life — and has to be stopped immediately.
If physical discipline won’t work for being mechallel Shabbos, it won’t work for playing with fire.