I had always understood that it was to do with how much the 'bit' can jump about in the hole as it's struck. Triangular profile holes are more common when hand drilled due to the non-uniform and jiggly nature of the human arm/hand/bit combination.
Mechanically drilled triangular holes are generated by the same principal, with a slack chuck or wobbly operator leading to the bit jumping about more and cutting the hole into the reuleaux triangle type shape.
I don't believe the triangle shape itself is a product of the turning of the bit through 120deg. It is unlikely that a turning round bar will produce a slotted hole (2 corners) as that requires regular 180deg turns which a drill should not do and requires movement on effectively 1 dimension only. 4 corner, or square holes probably are not geometrically stable as the bit is not able to find the corner easily each time due to shallow angle and are more likely to wear the hole round again but be over sized. I would hypothesise that the rounded corner triangle is the only possible shape (other than round) that a freely moving round bit with a chisel ground head can produce when using a machine or operator that avoids striking at 180deg for each subsequent blow.
Although as I have no background in either drilling or mining I may be wildly off.
Not seen the sun for months. Now evolving to see in the dark.