Why are Technic holes slightly smaller than studs?
I'm going to guess that when axles were first introduced Expert Builder was not a thing and the hole size was based on making a convenient path through the 4x2 brick that was the only thing with holes in it. Those holes do not work with studs, they are too large. Even the "new" 1x2 bricks with hole type 1 and 2 didn't accept studs (and the gap/slot at the top prevented it). That allows axle slop, but with the huge parts at that time this was not a problem, in fact it meant low-precision models worked just fine.

In 1970 there was the "Gear Supplementary Set" and "Gear Set with Motor" that had the first mention I can find of axles and gears.



Note that the set is labelled "Universal Building Set" and TLG appear to agree that "Expert Builder" appeared after that in 1977. In 1976 when the 695 "race car" was released it used second variant red axle stops and 1x2 brick with hole type 2 but wasn't Expert Builder.

The 1x2 brick with hole makes it clear that putting a stud in the hole was not possible (this may be the reason for the slot?)



AFAIK those bricks and axles are compatible with current Technic (they work IME but the dimensions might have changed a tiny amount and I wouldn't know)

Then we can look at TLG's current view of their history and see this from "The beginning" of Technic


  In the early 1970s, Jan Ryaa was one of the very first LEGO designers to play with the idea of building cars, using large square LEGO Mobil bricks in yellow, red and blue with white cross-axles and cogwheels. These were used for showroom models and were not planned as production models, nor intended for sale. 


I suspect he was using the production axles and bricks, but trying to make more mechanically accurate/challenging models and found the giant gears and 4x2 bricks a bit useless.

Brickset's history of Expert Builder makes it clear that by the time that theme was launched the "modern" Technic brick was in production. All four models used those bricks, and the hole were as compatible with studs as they are today.

Again, I can't find an official statement from TLG on this, but I will guess that since Expert Builder used existing axles they just ran with that size, only tightening up the hole a little to make their tiny-toothed gears work properly.