There is a things in the 5e thats is not very logical. On of them is Charisma based Intimidation, what if BG 3 used Home rule for this and it will be STR based?
No, if anything it should be a combination of Charisma and intelligence. Strength has nothing to do with intimidation. So what if you can lift heavy shit, and swing big weapons. Without intelligence and force of personality you won't know how to intimidate anyone and others will perceive your intellectual weakness and just trick you.
The game gives Barbarians specific intimidation dialogue not based on strength but the force of personality brought on by their rages.
I totally agree.
This game gives Barbarian only a situation advantage for Intimidation checks and that has nothing to do their STR ability. There is nothing preventing a Barbarian player from choosing a low STR build.
High-level spellcasters can summon and/or control high-STR creatures. There is really no logical reason for them to be scared based on someone's STR score. On the other hand, they have an easy time to make high-STR enemies (who are typically not spellcasters) delusional, frightened, fearful, intimidated, etc., unless something prevents that from happening.