Where is the principle derived from?

The definition of GTO or playing at equilibrium is where each hand combination plays to their maximum EV.

Why is max +ev the aim?

The goal in the game of poker is to win as much as possible. Because of this you want to take the highest EV line as that means you win as much as possible.
Playing a +EV line will still win you money, just a lower amount.
If you do your job, would you prefer getting paid your maximum or would you be satisfied with just a lower amount?

Playing to win the max EV isn't always done though. When all players play equilibrium then every hand combo is played to it's own maximum EV which results in a max EV strategy. When one player deviates from the equilibrium they become "exploitable". In the sense that the other player can change their strategy to increase their EV. Most players understand this and go for a maximum exploitative strategy, one where they take the highest EV line. You see this in hand histories throughout the forums as well. "Underbluffs so never bluffcatch"; "He's a station so never bluff". These are strategies that go for the maximum EV.

There is another option called Minimum exploitative strategy. I go over this in This video. The problem with maximum exploitative strategy is that your opponent can catch on quite fast to what you're doing. And when they then adjust you are losing a lot of EV. It is even so in the toygame I presented that if you play the situation 50 times, you maximum exploit 45 times and your opponent counterexploits just 5 times. Then you are losing money.

Minimum exploitative strategy builds the opponents mistake in it's calculations of your own frequencies. Making it less likely your opponent notices. And you being able to do the exploit longer. Which will still mean you earn more money eventually. Just not right now.

When would you choose which strategy? Maximum exploitative is the way to go if your opponents won't adjust. This can be due to different reasons. Either you don't play enough hands with them for them to notice (live play or large player pools (microstakes)), or they aren't good enough to notice and counteradjust.

Using rng for range is confusing when players use a random number generator. Had to read it twice for it to click :D.

I wouldn't say it's that abstract. There are two really good lessons to learn from this.

1) When someone needs to turn made hands into bluffs it is natural to defend below MDF. See True MDF. Got to keep that in mind when playing. You don't even need to think about your opponents range. When you now bluff or not you likely think about the likelyhood your opponent calls. Now you know your opponent should fold a bit more.

2) Betting as big as you can with nuts is common knowledge. How to maximize EV by betsize selection with non-nutted hands isn't. Now you can dig into it! Estimating the hands equity against your opponents range is indeed an estimation. Yet you'll be close to optimal if you know what to bet when you estimate 80÷ equity and it turns out you had 85÷. At least better than having no clue and just using a betsize at random, or based on solver output and having no clue why it uses that size.

It's also interesting to see that a solver selects the betsize for each combo and mixes bluffs in. No mixing of value hands in different betsizes. This likely is different when we allow raises.

Hint: I suggest you work out some optimal betsizes for different equities, plot it in a graph and look at the results. It's good to get a feel for the optimal betsizes.

I replied in the DM, answering here so other people can see as well.

This idea of nutted hands wanting to bet as big as possible only exists if your opponent manages to call MDF. Minimum Defense Frequency is calculated by 1 - (bet/(bet+pot)).
When we bet 2 into a pot of 1 our opponent will call 1/3rd of the time: 1 - (2/(2+1)).
When we bet 20 our opponent will call 4.86%: 1 - (20/21).
You can put those in your equation and you'll see that betting 20 is more profit.

The issue is that when you bet 20 and your opponent never calls. Then he doesn't reach MDF and the entire idea crumbles.

It is similar, yet for other reasons. At least that's how I use it.

If you have advantage in a part of the equitycheck range, meaning you have those hands and opponent not, then you likely want to bet within that betsize.
If you have more nutted hands than your opponent you tend to go really big.
If you have more medium hands than your opponent (rest somewhat equal), you tend to go smaller and bet more often.

A very general rule is also to bet flop small and often.
On blank turns you go big size. On not blank turns you need to evaluate.