I agree, but to me the only reason for porting battleaxes is to retain the more "bulky" texture. My suggestion would be to make some factions have normal axes (possibly with nerfed combat stats) and some factions have battleaxes with better combat stats, but sacrificing the ability to "peel" wood, and taking more durability damage from cutting wood. The factions with dedicated battleaxes would then use vanilla iron axes as woodcutting axes (that doesn't seem too non-canon to me).

I'd rather kill enemies with battle axes rather than some sort of root and tree ax, no exaggeration. I prefer to import the axes as before, that is, let them give us everything and let the vanilla axes use nerf so that they would be used for what they were created for, i.e. chopping wood. Of course, you can also kill with an ax, but that is why battle axes were created to be more effective.

They could add battleaxes as bearded axes (example here), the beard(which is the part of the axe blade that hangs down) was intended to act like a hook and was used pull away shields or weapons, so why not give them the ability to be break shields and remove that ability from the regular axe.

I'm not sure about that, I like the Vanilla change, what's wrong with the vanilla axe, and plus that means mod team have to change vanilla data, which, by the way, is not going to happen