My formal education is in analytic philosophy, with at least a mild focus on logic, so I want to point out some concerns I have here with the argument.
(Edit: note, I'm being absurdly nitpicky here, please don't take this is criticism of the general thesis, just point out some technical issues with the argument):
We can all agree that the primary challenge in golf is the fact that we are manuevering a ball by playing a stroke across a distance. The farther Point A it from Point B the more potential strokes we need to play to get there.
This does not actual follow. You have slipped in an axiom that more distances implies more potential strokes. Imagine we have a 400 yard wide open par 4, and a 125 yard par 3 that is an island green with the diameter of approximately one yard. There could be times when terrain dominates distances with regards to potential strokes. If you are going to make this argument, you need to set it as "
all things being equal more distance means more strokes" which is still dubious in practice (I find a 60 yard shot to be more challenging than a 125 yard shot, but my short game is terrible), but I'd generally agree to the axiom.
Therefore, it is axiomic that golf is judged by using the least strokes per unit distance - whatever that may be. This can also be stated that the higher the average distance per stroke, the better the score.
This proposition does not follow directly, it will only follow "all things being equal," that is "
given the exact same course at different distances, golf is judged by using the least strokes per distance," which is a very different statement. The argument will eventually form "distance is always an advantage", whereas here I think what follows is actually "closeness is always an advantage," which are two subtly different things.
You have no control over your luck - but you do have control over your expectations
There is a long conversation here about what you mean by luck, but seeing as you mean luck-in-dispersion-pattern, I think the statement is fine
which is why avoiding penalty shots becomes an axiom,
I know I'm being absurdly pedantic, but axioms are by definition arbitrary. Trying to justify them will be circular. I think point you're trying to make here doesn't necessarily follow. I can think of some strange ways in which taking a red/yellow-stake penalty would be optimal vs playing it safe.
In the above Road Hole situation for me, the target on the approach really only changes as my disperson pattern changes with the club I'm hitting into the green, ceteris parabis, however, the angle from which I'm approaching that target may move the number of favorable possible outcomes farther away from the hole. Regardless of the location from the fairway I would still be selecting a target based on the left edge of my disperson pattern being away from penalties/lost balls. The only thing that changes is whether or not that dispersion pattern is more likely to yeild a tighter approach or not.
The thing that changes the disperson pattern is the club. The thing that changes the club, ceteris parabis, is the distance from the hole.
Distance. Always. Is. An Advantage.
Again, I don't think this actually follows. I think what would follow is that "all things equal, closeness to the hole is always is an advantage" if we assume that shorter shots/clubs always have a tighter dispersion pattern.
Anyway, I hope this is taken as friendly. I'm not trying to be an outrageous pedant, it's just how my brain works.