We have a vintage, original to the house, Thermador bathroom wall heater...I'm sure they are dangerous, a kid can stick their finger through the grates or bump up next to the extremely hot face plate...
True BUTT only once!
If it takes more than once then maybe we are hoping that Darwin rears his ugly head and pushes the Natural Selection button to rectify the situation.
Seriously, keep the heater if you want but the GFCI is a MUST! Regardless of electrical code mandates, it is your families personal safety that mandates installing the GFCI.
What *I* would do is use ceiling mounted quartz infra-red heat. Then remove the wall heater, install a wall mounted towel heater above the hole using existing wiring as needed, install the GFCI, repair the wall hole as needed.
Believe it or not, towel heaters are VERY nice!