Vibration.
When you
chop using a knife, your arm and shoulder muffle vibration thus reducing the amount of shock to the knife.
When you
baton using a knife, there is very little to reduce vibration so your knife takes more shock.
This adds up over time. Any knife and any steel will eventually develop microscopic stress fractures as a result of shock. One day, these stress fractures will break completely, and your knife will be ka-put. The only difference is
WHEN, never
IF. A "winchester" skinner from Walmart will probably not last long. A Busse Battle mistress will take the abuse for a long long LONG time ... but it too will eventually succumb.
That's why I just cant view batoning as anything other than shortening the life of a knife. Yes, you may be able to baton a great knife regularly for 15 or 20 years ... but eventually it will break as a result of it, whereas it would have outlived you if only you had treated it properly. A knife which is used properly (you know ... to CUT things) will ware out long before it ever breaks.
You really don't need to cut or split any wood unless you're in a very cold wet situation. Just break what you find, burn it in half, etc. That said, processing wood is fun. It's a guy thing.
That isn't the half of it.
How do proponents of batoning think that their ancestors have been splitting timber for the last 10,000 years? Ill give them a hint - they weren't using their ESEE or their BK9.

They often didn't even use an axe. Wooden pegs and a wooden mallet are all you need to split even a very large log. Now, I suppose you could use your belt knife to whittle the pegs, but beyond that, it needs to stay in its sheath.