What if it's decent steel with a good spring temper?
I have a hatchet from the €1 store that I assumed was a piece of shit.
The handle is some bright yellow Chinese semi-hard wood similar to Birch and it came with a terrible grind.
I threw it in the back of my truck where it sat for years, gathering dirt and rust.
I threw it at shit, chopped right into brick, used the poll as a hammer to drive nails, used the bit to pull out said nails, chopped through steel wire and tie-down straps, opened cans, pried open crates, busted pallets, chopped the roof off a car, etc
Then I decided to take an angle grinder to it and give it the narrowest, sharpest edge I could, just to see if it was possible to shave your face with.
And guess what.
It threw a shower of high carbon sparks the second it touched the grinder.
And it took a beautiful edge.
I keep it in my summer house now and it's a joy to use.
It has a better edge than my Wetterlings did from the factory.
That said, it took a lot of work and fine tuning to get there - depending on the person, it may or may not be worth the work.
Pic related. The €1 euro axe.