Random comments.
First, re the "there should always be a chance because a PC invested resources in this."
No, there shouldn't. The fact that a PC invested resources in Intimidate doesn't mean that fairness dictates that every specific situation have at least some chance of Intimidate working. It means that the game, overall, should have chances for the PC to use his skill. Try applying that logic to other things- if I invest lots of feats in improving my Bluff skill, I still fail when I try to convince the Duke that he's really a frog. Likewise, if I invest lots of feats on my Intimidate ability, it still doesn't work when I lack the leverage necessary to make credible threats. A high modifier and a high die roll should not replace these things, they should augment them, much like any other social skills.
Second, regarding the idea that intimidate should be "convincing people of things through the use of fear."
I think its safe to say that convincing people to do things through fear is something with a LOT of subcategories. And I don't think they should all be treated alike. Convincing someone that you will break their arm if they don't comply is one subcategory. Convincing someone of the truth of their secret fear that their wife is having an affair is another. You don't intimidate someone into believing that. You might insinuate, you might suggest, you might exaggerate, but you don't intimidate.
Finally, re the idea that coercing through threat is not enough ground for a skill to cover.
Really?
First, re the "there should always be a chance because a PC invested resources in this."
No, there shouldn't. The fact that a PC invested resources in Intimidate doesn't mean that fairness dictates that every specific situation have at least some chance of Intimidate working. It means that the game, overall, should have chances for the PC to use his skill. Try applying that logic to other things- if I invest lots of feats in improving my Bluff skill, I still fail when I try to convince the Duke that he's really a frog. Likewise, if I invest lots of feats on my Intimidate ability, it still doesn't work when I lack the leverage necessary to make credible threats. A high modifier and a high die roll should not replace these things, they should augment them, much like any other social skills.
Second, regarding the idea that intimidate should be "convincing people of things through the use of fear."
I think its safe to say that convincing people to do things through fear is something with a LOT of subcategories. And I don't think they should all be treated alike. Convincing someone that you will break their arm if they don't comply is one subcategory. Convincing someone of the truth of their secret fear that their wife is having an affair is another. You don't intimidate someone into believing that. You might insinuate, you might suggest, you might exaggerate, but you don't intimidate.
Finally, re the idea that coercing through threat is not enough ground for a skill to cover.
Really?