As you can see, I don't agree. Deciding on an approach to a negotiation or seduction attempt seems quite analogous to me. (I've already said why this doesn't apply to physical stats; everything you do with those is dependent on die rolls when at the level they matter at all in a way many people wouldn't tolerate with the mental stats.)
I think you are combining two very different things. I believe there are two different categories of "come up with a solution" to a problem:
1. It's simply a plan that may or may not succeed. "I know! Let's build a giant wooden horse..." Similar to the Wisdom examples discussed above, I don't know how it's possible to describe a plan as "smart" or not. Whether or not it
works is going to be up to how the GM adjudicates it, and whether or not it does or does not work doesn't necessarily mean it was or was not a good plan.
And, yes, that becomes subject to all the risks you describe: maybe the GM is more likely to adjudicate it positively because it's his best friend's idea? Maybe the player thinks it's a stupid idea, and they are proposing it because they are roleplaying? How on earth do you judge things like this? I don't think you can.
Similarly, maybe the player of the low-Cha character believes their grandiloquent speech is exactly what an overconfident schlub, blind to their own toxic personality, would do?
I just don't know how you determine any of this, or decide what is good roleplaying and what isn't. If the GM is too easily persuaded by player personalities that's not a problem with the game.
2. The challenge HAS a specific solution, such as the "code" to a puzzle, or where to look for the McGuffin, and the player of the low Int character figures it out. There isn't a
probability of success: it was correct.
That second category is where I was saying that I don't think there's an analogue with the other stats.
Except that I just thought of one: lie detection and Wisdom. About which I feel just a strongly. (That is: using Wisdom/Insight to "detect lies" is not at all how I want to play RPGs.)