Here's where I stand on the issue.
I think the main thing is, people confuse "being intimidating" with "Intimidate," so to speak. Understandable, given that I'm using the same word twice.

Here's the difference:
"Being intimidating" just means you're making someone or something afraid of you. Not much to it--you can do it to puppies and small children, no matter how weak or powerless you are. That's what most people are referring to when they talk about how a really strong guy "can be intimidating." So can an angry mob with pitchforks and torches, too. Or a rattlesnake. Or a really high cliff.
Intimidate, however, as a D&D skill, is a rather advanced
social skill. You're not just making the guy crap his pants in sudden fear--any monster can do that. What you're trying to do is elicit a very specific and persistant response from a person, using fear as the stimulus. You have to be good enough at Intimidating that the person will continue carrying out your wish, even when he's out of arm's reach. The effect is somewhat like a light version of the
charm person spell, wherein the person will act as though he is your friend, or is friendly toward you. The same with intimidate--but instead of 'feeling' that he's your friend, he just knows that he has to -act- as your friend, or face the consequences.
The trick, though, is that there is a very specific response you want from the person, such as the answer to where the Tome of Unholy Puppykicking is hidden. Now, if you just make the person
afraid, you might get all sorts of responses. He might soil his pants and start blubbering incoherently. He might run out the door. He might start yelling for his bodyguard in the next room. He might cast Fireball. Or--worst of all--he might lie to you, and send you walking toward the nearest dragon's den instead. You've made him
afraid, but without the social ability to manipulate that fear--or to figure out whether you've really accomplished what you wanted to do--you're not really any closer to your goal.
Now, being strong--being able to threaten someone with physical violence--is one threat to use. But it's not the only one, and certainly not the best. So a high-STR character would probably use threats of physical violence as the 'stick' in his Intimidation technique. But a halfling rogue might imply, instead, that if the guy doesn't give up the info, he might someday wake up to find his barn burnt down and his daughter pregnant. Or a LG paladin might imply that if the person doesn't comply, the Church will be "very disappointed" in him, having serious consequences to his social status. They're all using whatever abilities or traits they possess, in forming their
threats--but actually getting the response they want out of the person, is a
social skill. A CHA-based check.
Certainly, it's well and good to give circumstance bonuses for an appropriate display of strength, if that's your preferred method. But there's no reason to unduly reward high-STR characters (by making STR an acceptable substitute in the check itself), as opposed to potentially intimidating displays from high DEX characters ("I throw a dagger into his chair, inches away from his crotch"), or high-INT characters ("wait, wait, what's this in my pocket...oh, I see, it's a FIREBALL spell..."), in Intimidation checks. There's no sense in swapping the core ability for the check, when the game already lets you use your strength (or dexterity, or intelligence, or whatever) to benefit the Intimidate check using a "favorable circumstances" bonus.
So, I think the best way to treat it is, Intimidate itself remains a CHA-based skill--because successfully using fear to your advantage requires a bit of deft social handling. But STR, along with any other attribute, can potentially be used to gain "favorable circumstances." This accounts for the fact that physical strength is not going to be universally fear-inspiring, any more than any other personal attribute might be. The hill giant isn't going to be impressed by the widdle human smashing a widdle table over his head, any more than the archmage is going to be too fearful of your l33t fireball.
Of course, this requires players to actually -think- about how to create favorable circumstances, aside from simply looking for the nearest table to smash over their heads. Which is probably the core of the issue.