I would suggest that an axe with a chip out of it leaves a crappy signature, like a bad pen.
instead of seeing the quality of the axework, you see the scratches left by the chip.
I had a 12 inch north american style broadaxe, I cut it down to a 9 inch and it's still to heavy for me compared to my Austrian goosewing... what a wimp!
I would not try to restore a broadaxe or any tool with rust pitting on the back, or flat side of the blade. Some pitting on the bevel side is not a big deal.