The idea would be that you would choose an appropriate base level and level up rate for the intimidation stat the same way you would every other stat. On a per species basis. If you could have a single mouse that was incredibly well equipped with magic abilities and a single dragon with low stats all around or some other random configuration of stats and skills, then intimidation as a stat wouldn’t mean anything. That’s only the case if stats are random. The case is probably that each species of monster is designed with a specific set of skills, stats, and personality.
There main downside to simulation, (used alone,) is that it may become too mechanistic and symmetrical. Intimidation involves perceived danger, not actual danger. Intimidation allows you to factor in an extra variable for more realism. It depends on the combat system, but I can imagine cases where it would be terrible. If it were one of those games where enemies take turns hitting each other, have the option to retreat, and disappear after the screen fades to black, then the game would be too frustrating if the enemy ran away every time its HP was brought down to near zero. If it were an open combat system were enemies could run around, then you would have enemies that would constantly flee from an opponent and an opponent that would constantly chase the first monster. You would end up with chains of monsters running around the screen and little actual fighting.
You really don’t want the computer players to be omniscient. A better method is to use fuzzy logic. A strong intimidating monster may chase opponents weaker than it, a timid monster would avoid risky conflicts, a weak intimidating monster would “trick” it’s opponents into avoiding a fight by bluffing, and ordinary monsters would pick fights with either slightly weaker or slightly stronger monsters based on apparent risks and rewards. Their own aggressiveness/timidity would determine how risk averse they were and their opponents’ intimidation factor would determine how strong their opponent appeared to them.