I'm an idiot, sorry)) I thought that "inviting a hero" in HD meant the same as buying him.
The original idea of the HD mod was that there should be no advantages, except temporary ones, compared to the original.
Although, for example, in HD they fixed the bug of selling artifacts at inflated prices. They also fixed the issue of leaving a hero without an army by transferring it. Although the Chinese actively use this when completing the game.
By the way, I already asked a question, but didn't get an answer. Nasos, what do you think about selling artifacts at inflated prices? Is it a bug or an atmospheric feature of the original gameplay?