Psychological Mafia

But this is just a specific case of a regular Mafia game.

That's not entirely true.

Individual Mafia games with clues will hardly differ from those without clues (like the last Vis).

Did you read the example given in the first post of the thread (although, I can't be sure that all aspects of this type of game were used there, but the main idea is clear)? These are completely different games, differing in more than just the presence or absence of clues.

It is intended so that it can be played in parallel, but our modest experience with such games suggests that this is not the best idea.

Why?

And the main question: how many people will want to participate in such games, and how many will want to run them? I think that, given the choice, most people will prefer the classic Mafia game.

We won't know unless we try. On a neighboring portal about Heroes, for example, they only play the psychological version of Mafia. You can ask Neyra, Vervolki, Cash, and the others who have played or are playing there. I don't think they would play there if they didn't like it.