Damaged tangs suggest to me heavy-handed use – a machine-shop operator who is drilling holes and very likely wishes he wasn't but has to make a living somehow, is less likely to treat the company's tools and machines as gently and lovingly as we in our home workshops who have had to pay for the equipment. Blame ye not the tool, but the user.
That's an interesting suggestion, Martin, that the tang aids making the drill itself. I must admit I have never seen any description of how that is done, but you might be right. Nevertheless, we are considering the use of the tool, not its manufacture.
I have augmented my library of model-engineering books with ones written for the engineering trade – very much harder working conditions for the tools. This quote is from one of them, a text-book for engineering college students and reference for professional machinists:
The action of the taper is to wedge itself into the drilling-machine spindle, which has a taper to suit… The greater the pressure the tighter the drill, but even so, it is necessary to provide a positive drive in the form of a "tang" which fits into a corresponding slot in the machine spindle.
Sandy, A.H., A.M.I.P.E., "Cutting Tools For Engineers" , Crosby, Lockwood & Son Ltd, London {date not stated], Chap VI "Drills & Drilling" pp 56-70.
The title page informs us that Mr. Sandy, a "Silver Medallist, City & Guilds", was an "Instructor and Lecturer, Mechanical Engineering Department, Borough Polytechnic, London." I think we can, and I certainly do, accept that he knew his subject.
Also, I pointed out that if the tang was purely for ejecting the tool from the spindle it would not need to be made so elaborately, to fine limits prescribed in the official, industrial standards.
The quote itself is from p.57; but even given that the pages are slightly smaller than modern A5, that page range shows there is more to drills and drilling than might be obvious. My omission ("to suit…"
is of just a reference to adaptors.
Why lathe tailstocks do not normally have tang-slots, is another matter, and I have often wondered that. It is a nuisance when using my tailstock die-holder in the ML7, as the taper does not provide sufficient grip. On the other hand, it does not fit the Harrison L5 tailstock as the tang hits something – the end of the barrel screw, probably.
I can only suppose that lathe designers assume a hole too large for drilling from a Jacobs-style chuck that fits the tailstock, will be bored to size from a pilot hole.