I’m afraid we may be conflating CR and intimidation, to a degree.
If T-Rexes still existed, I would stay the heck away from them even if they just walked around silently, no need for them to roar or be scary, because a T-Rex is obviously of a much higher CR than a regular unarmed human.
Now, intimidation tactics do exist in the animal kingdom, evolved strategies meant to make a creature look more dangerous than it actually is.
I believe that this is what the intimidation skill should be about: a successful check makes somebody appear more dangerous than it actually is, a failed check does the opposite.
A classic example of a failed check would be the low-cha 20th level monk sitting in a bar, getting harassed by hooligans. When the monk tries to shoo the low-insight hooligans away, he fails the check and then has to wipe the floor with them in the resulting fight. The low cha monk failed to telegraph his actual power, and a pointless fight is the consequence.