The thought is a good one, but the problem is that the end that is hammered flat would make the hole for the bench dog bigger than the rounded part of the shaft and the hole and shaft of a bench dog being tight is what makes the dog work properly, so the flattened end being bigger than shaft means it wouldn't stay tight in the bench dog's hole in workbench.
First, its my opinion that the item is a hand wrought bench dog...therefore I my position is as follows...
What we don't know is the purpose for the flattened end of the shaft...its probably serves multiple purposes...
In many cases, the shaft of a bench dog's shape and holding power is based solely on the thickness of the bench top or vice itself and the thickness of the board or item being held, and not necessarily on the bench dog's shaft shape or dimensions.
Many woodworkers make their own tools and accessories, and some of which may be modified for multiple uses, hence the flatted end.
The dimensions of the square or diameter of a round dog hole also plays a part in the holding power.
As an example, the holes in my carver's bench top are 3/4" square X 2" deep, and the holes in the vices are 1" square X 8" deep...either of which could utilize the hook shown above.
However, I prefer to use my handmade walnut or maple bench dogs.
I custom-made my own 3' X 8' carvers bench using 8/4 X 8" Maple with 3/4 X 2" Walnut dog bands, and end and side vices using 8/4 X 8" Walnut double faced with 1/4" saddle leather, and home-made screws, double guides and handles.
I find that there is less damage using wooden dogs as opposed to steel dogs...(although I have both)
Therefore my vote is for bench dogs.