I'm curious about why Fender changed from using a four bolt neck mount to a three bolt neck mount sometime back in the sixties or seventies and then decided to change back to the four bolt mount. What advantages does one mount have over the other?
The 4-point joint was initially chosen, quite reasonably, to provided strength and solidity.
As a consequence, the only way to change the action (distance between strings and neck) was to use the tailpiece saddles. It was as if the neck was glued to the body, like e.g. a Gibson, although you still had the option, if it was absolutely necessary to change the angle of the neck, to unscrew the neck, place some filler on one side or the other, and screw it back.
At some point, partly to make it easier to change the angle of the neck, and partly (some would say "mostly") as a marketing gimmick, they changed it to a 3-point system, which made it easier and faster to change the angle between the neck and the body. You did that by loosening one of the 3 screws, adjusting a smaller internal screw that forced some distance between body and neck, and then tightening again this third screw to lock things in place.
You could even do this without losing the tuning of the guitar: adjust a little, see how it feels when you play, adjust another bit, see how that feels, and so on until it's just right.
This new system however proved to have many defects: less contact between neck and body and therefore less resonance, weaker neck-body joint, loss of grip of the screws in the wood after repeated adjustments, and so on. And all of this for something (the ability to change the neck angle) that should not be needed at all if the instrument is designed and built properly in the first place.
By and large, sensible owners avoided using this option at all, and kept the neck flush with the body, to achieve maximum contact, strength, and resonance.
Eventually, the company realized that the whole thing was a liability, the novelty effect had also run its course, and so the more sensible 4-bolt system made its return.
A plane is defined by three points, so I'm not sure you gain much from the fourth screw, and your screw costs go down if you're using fewer per instrument. I don't know if having one more screw of tension is crucial; I've seen between 2 and 6 screws on old guitars on Reverb.
But the key thing is that the change came with Micro-Tilt, which allows changing neck angle without shims. I've never owned a guitar with Micro-Tilt, so I don't know how it works, but I've had to shim my Tele to get a decent action, and I think it's a thing we should have.
But, as a community, musicians are conservative, meaning they like what they like and don't want to change. "It isn't like Leo Fender made it and Buddy Holly/Hank Marvin/Dick Dale/Jimi Hendrix played it", so they went back, eventually making a four-screw Micro-Tilt neck.