NHF – new heroes for Heroes V 3.1.

I agree, I'm in favor of having a structure, and it makes sense when one skill is a development of another (for example, Storm Wind from the Lord of Storms).

In the old skill tree, that's how it is. But again, this is an aesthetic connection, not a mechanical one.

Some skills are simply impossible without a connection (enchanted ballista, exploding corpses, etc.).

If there are only 6 skills in a school, and they don't repeat each other in the order they appear, the amount of randomness will be small (but is that really the case?).

Added after 3 minutes

Perks are arranged in structures with connections not only for beauty and order, but also to reduce the amount of randomness.

Actually, there's no beauty in it. When it's illogical for one skill to lead to another.

Regarding randomness, we need to look at the repetition of skill appearances with 6 skills.
If they are constant, then we need to look for a different scheme.

Added after 5 minutes
As I understand it, when leveling up, the game doesn't care whether it's a level 3 perk or a level 2 perk that is being upgraded (the difference is only between level 1 and 2/3).