I use centre drills all of the time, usually as a pilot drill in the lathe to give me a good starter for a larger drill. However, whey are they the profile they are?
A combined countersink and drill used to prepare work for mounting centres.
Also used to pre-drill holes for subsequent drilling operations. The centre drill is very short resulting in it being stiff and so not easily deflected when making the first pilot hole.
Once the workpiece has been drilled with the centre drill it can then be supported with the centre that is held in the tailstock.
The void formed by the parallel part of the centre drill ensures that the point of the centre is clear of the workpiece and is supported on the 60° taper.
If the point of the centre were to locate on the workpiece then it would run out of true and damage the centre.
The void also is a cavity for oil so ensuring that the centre is lubricated.
So, quite frankly a very simple concept and the profile of the centre drill is very obvious.