Under the "Player Game Plan" tab, I have the bad habit of clicking the "save to all defenses" button when I adjust a player's distribution. Now any smart coach in real life wouldn't go about this approach when preparing for their foes, and I'm assuming that's true in Hoops Dynasty as well for the experienced coach. I just haven't graduated to that level yet, or at least haven't thought much of it, or am just not quite sure how to adjust to maximize an offense.

Has anyone done "data studies" on this?

I'm aware that a lot of giving a player more or less distribution depends on the opponent's defensive abilities, but in a general sense (against an average team), what are your impressions?

I always save to all defenses when changing distro.  But I also know that I dont gameplan daily as much as some other coached.  In general I view distro as how I want my offense to run, and that doesn't change against most defenses.  So the only time I change distro for 1 game will be when playing against a man defense with a really bad defender somewhere that I can take advantage of.  But ideally mo offensive game plan doesnt change from game to game.
but I dont know what kind of studies you want to see on the subject.

I definitely change my gameplan approach depending on what type of defense I'm facing. In very broad terms:

M2M - as OP said, find the strongest / weakest starting defenders on the opposing team and reduce / boost distro to your players accordingly.
Press - Give more distro to players with high BH / PAS.
Zone - lots of zone teams always play either a 3-2 or a 2-3 and never switch it up. You can use that to your advantage by changing the distro for your 3PT shooters accordingly.

There are a lot of other factors related to your opponent's D, but these are the first things I look at.

Backwards Nirvana, any symbolism to that?  Anyway, I do the same thing when I change my distro, I always just hit the Save to all defenses button.  Then the next time I want to change my distro, I just hit it again.  Rinse, wash, repeat.  I do it every time I make any change to my distro, no matter how small.  Wouldn't sweat it much.

I save to all defenses too, except if I am game planning in a certain way for a zone team. If I change the dist against a zone team, I don't save to all, but I use the same dist against a FCP or M2M in general.