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batoning memeing aside.
the only thing ive found where i find light batoning preferable is actually on fatwood.
although the dust that a saw will create can be nice but it is also very hard to position and easy to lose. and with an axe, even as small as pic related. it can be tricky to split it just right down to that lovely matchstick thickness. not that it cant be done, not at all.
but since fatwood pieces that you collect tend to be quite small, atleast they are around me, i find that a small batton tap with a knife gives me the precision i seek.
but that is about it really.
in my opinion even a small pocket/carving axe like pictured will vastly outperform a knife battoned through wood, in efficiency, ease of use and stress on the user/tool
but since it can be dificult to feather fatwood, i find "batoning" it into matchstick thickness bits to work great.
but doing it to get to firewood is just silly. sometimes very fun. but silly