It makes sense to fit a shaving point plug on them, Bednobs. It means that people who've got a shaver socket in their bathrooms can use them safely, whereas everyone else can use them elsewhere (again, safely) by purchasing a cheap adapter:
https://www.wilko.com/en-uk/wilko-1-amp-fused-shaver-adaptor/p/5363940
If they had a 3-pin plug on them, people without a shaver socket in their bathrooms wouldn't be any better off (apart from not having to buy an adapter), whereas people with shaver sockets might be tempted to improvise a connection between those sockets and their toothbrushes, thus putting themselves into danger.