Wife and I take 4 mile trail walks in this wildlife management area several times a week. On todays walk on one of the gravel roads I see a small piece of this object sticking up, looked like dirt bike tract uncovered it. Normally I'm pretty decent on identifying old parts (because I'm old). This part is all solid steel or iron, no threads, small machine notch on small end, looks to be some hammer marks on the big end, I will look again with a magnifier for any numbers. This is what it looked like after some time on a wire wheel, as found it was covered in a thick layer of rust and crud, about 3 in. long.
If it was threaded on the small end, I'd say it was a small spindle for a wheel bearing. It looks like it has a shoulder for the bearing to ride on. It doesn't look anywhere near old enough to be prior to threaded retaining nuts though.
Seriously... a nail driving tool? Not to be confused with "anal driving tool". The small end is concave to keep it centered on the nail head. You hold it in the middle and whack it with a hammer on the large end. (Which shows signs of being hammered.) It would help you drive a nail with a large hammer and offer some protection for your thumb.
No threads or teeth were ever on this thing, pretty sure it is very old judging the condition I found it in.
There are tons of different styles & shapes as the machines have evolved over the years. They usually don't have threads; they snap into a collar that is placed in the holder on the drum or rotor first. I changed many when I worked for a County road district here in Oklahoma. That photo is just one I quickly grabbed to show the general shape/design. The one you found is VERY worn - Gary