This is why God invented luthiers...there are good reasons to pay for expertise.
I go to the extent of regrinding all my twist drill bits to make them more appropriate and safe for drilling wood. Standard bits are designed for drilling steel and the flute geometry is too aggressive for wood, brass, or Plexiglas/acrylic.
Regrinding drill bit angles for wood use is a good idea, but doesn't guarentee other luthiers do the same or follow proceedures to prevent slivers of wood from being produced where they shouldn't.
Awhile back i spent about an hour making and using a small sanding block to attach to the end of a shaped piece of closehanger, in order to reach inside the soundhole and carefully sand off pretty good sized slivers of wood around the bridgepin holes of one of my favorite ukes. I've seen this on otherwise well made acoustic guitars also.
I suspect an overly aggressive drill bit flute angle, or a little too much drill speed or pressure caused this when the bridgepin holes were cut thru the top. I would guess it's pretty common, since it's generally out of sight.
As a practicle matter the uke sounded the same even after i removed the slivers of wood, but it bothered me when i was fitting new bridgepins and saw what looked like the underside of the top needing a hair cut! This was on an over $1000 uke,....so it can happen to the best of us,.....even luthiers.
BTW,.....i've drilled wood over decades and never recut my bits, as i also used them for soft metal work in gold and silver projects. But when i used them on wood, i went really S-L-O-W, and stopped when the drillbit just started to exit. Then either drill from the other side to meet up, or hand ream the exit hole to complete the hole. Another option is to put a piece of scrap wood behind the piece of wood you want to drill. It's presence there generally stops wood exit slivers from happening, but you don't always have that option.
When i worked on jewelry, drilling multiple very small holes in gold (size 62-70 drill bits) required patience, as the bits were fragile and prone to heating up. The holes were needed as a 1st step to set diamonds into, but if you tried to drill too fast a drill bit would break off in the hole.
Often it couldn't be removed easily(was below the surface), and you'd have to soak the jewelry item overnight in a water/alum solution to rust the steel out of the hole. (an old watchmaker's trick)