Why are we not generally using egg in Buckwheat crêpe (or galette) but only in Wheat Flour crêpe?
Eggs make crepes stronger, which makes them less vulnerable to tearing. It also adds some taste if you like eggs. 

If you have a good frying pan then you don't need them at all. You can make crepes with next to any type of flower without eggs or any egg replacement. Pure buckwheat on the other hand does not have gluten and might be more fragile.

In my experience "galettes bretonnes" are always with eggs, water and buckwheat, but without white flower or milk. I expect here the eggs are especially in use to make the dough less fragile.