I made a 4 and a 5mm hex broach this morning.
I used silver steel and tried them putting a hex socket in mild steel. The 4mm worked ok with a 4.2 pilot hole but when I tried a 4mm hole it took the corners off the broach. The 5mm was no better - even with a >5mm pilot.
I hardened the broaches in oil. I'll try water next to see if they do a better job.
Only takes a few minutes on the mill with my dividing head set pointing 2 degrees down. I put the cutting angle in the end on the lathe at about 8 degrees.
So far a lot of effort with little to show for it.
They work OK in brass but I've not come across many socket head screws in brass!
If the next, water hardened, broaches fail I'll try HSS - probably by silver soldering broken end mills into a 12mm shank.