I'm very late to this discussion, and it has been super - I thought I'd relate my centre drill and spotting drill experience...
Bert taught me to always use a centre drill on mill or lathe to start a hole because it is far more rigid than a regular twist drill, so it will help in starting a hole in a precise spot. True.
But I'm 'that guy' that questions everything (including myself), so I did a bit of research. I found a pamphlet (before the internet was wide spread) from Mitsubishi about spotting drills, and within a few months had bought one. Sadly that paper seems to be lost in time, but this one is almost as good:
In high precision machining, drilling a hole exactly where it is needed is a challenge. The challenge comes with choosing the right spot drill for your job.
www.harveyperformance.com
This one is a lot more basic, but their 118 vs 140 paper referenced at the bottom is the best I've seen
What is the purpose of spotting and center drills? Advantages and disadvantage of center bits compared to spot drills and which one you need.
www.finepowertools.com
To resume the story I bought an inexpensive (but still name brand) HSS spotting drill. This changed my milling and drill press game greatly. The spotting drill is easier to see around when using a loupe to verify location. It is rigid, and makes the perfect hole to start the drill. Since then I've bought cheap offshore carbide ones, and name brand ones and they all work great.
Their use in a tailstock to start a drill operation makes sense also. A spotting drill is closer to the length of the next drill to use, so there's less back-and-forth than using a centre drill.. Less plunging and edge catching too. For very small drills, I confess to using the centre drill nubbin to start things more often than using a spotting drill. old habits die hard...