Mixing Stats and Skills
First of all, on page 33 in the 3.5 DMG, there is a variant section that discusses using abilities with skills that they are not normally keyed to, and it gives a few examples. For instance, in the games I lead, PC's have often gone to a local library to research the various clues they've picked up. This created a "research check" house-rule that is a Gather Information check based on Int instead of Cha (and they don't have to pay any money). So to me, A character using Str instead of Cha for their intimidate checks seems to fit in with this idea nicely.
As for barbarians with a Cha of 6 who are dumb-looking, it is true that their screaming madly won't be that intimidating, however if this same barbarian had a 22 Str and managed to bend the guy's sword in half... that's a different story.
Lastly, the idea that this kind of intimidation won't work because it will just make the person scream and run away or faint or whatever, well that's what would happen if the character -failed- their Str based intimidate, just like if they failed their cha based one and the target wasn't fooled or scared by their threats, blackmail, etc.
J from Three Haligonians