No argument from me on any of this.
So how to fix, or at least mitigate?
You've already suggested divorcing initiative from Dexterity. Good idea. Divorcing offense in combat from Dexterity would be the next step, with the intended end result being that Strength helps offense, Dexterity helps defense.
Again, this comes with a serious downside that a lot of people do not want: it means that 100% of people who are good at combat HAVE to be more like Conan/AHNOLD than they are like Zorro/Errol Flynn. That's a sacrifice a lot of people aren't willing to make.
As a result, while I totally understand why you want to do this from a purely gamist standpoint, from a standpoint of capturing concepts and experiences--not exactly "narrative" or "simulation" per se, but definitely the aesthetic value of the rules expression--this is a sacrifice that is too dramatic to accept. If we're going to keep six stats, and one of those stats refers
specifically to Mighty Thews, then there need to be combat-ready characters who
do not use that Mighty Thews stat and instead use precision, deftness, speed, and mobility to succeed, not brute force.
Could perception somehow tie in to both Int and Wisdom? E.g. on an easy check you use the higher bonus, on a normal check you use the average of the two bonuses, and on a hard check (but not hard enough to give disadv.) you use the lower of the two - could that work?
Potentially. You might find the 13th Age approach to certain stat things interesting. There, your AC, physical defence (PD), and mental defense (MD), scale based off of the
middle of three stats. AC, for example, is Con, Dex, and Wis. You ignore the highest and lowest. This has the side benefit of making min-maxing no longer a trivial calculation, because you need
many high stats to have the middle stat be the best one.
If we did take this route, then perhaps Perception is a function of Wisdom, Intelligence, and Constitution--the latter because you need to be
awake and alert to detect things, and the ability to resist fatigue is usually tied to Constitution.
As for making Charisma more important more of the time, it'd help greatly if some 0e-1e conceits hadn't fallen by the wayside over the years. Charisma was the main stat in those versions for attracting and retaining henches, hirelings, and followers; all of which were rather important to one's career as both an adventurer and - later - as a domain keeper. And even with that, Charisma was often seen as the best stat to dump; I'm not sure that's ever changed.
In 5.5e a bit of this might be revivable via the Bastion rules, but that's again a bit niche and not all campaigns will use them.
Yeah this has much the same problem as carrying-capacity stuff for Strength. That is, hirelings, henches, retainers, etc. are usually really boring to manage, mostly just inducing craptons of paperwork. Yes, the benefits might be enormous--there's a reason Leadership was the single most banned feat in 3rd edition, since it literally gave you a second character--but the paperwork is not worth the reward.
If you can find a way to make hirelings a breeze for both players and GMs to interact with, without making them overpowered or unimportant, then I could certainly see this working out. As it stands, the simple reason this got left behind is because it wasn't worth maintaining, and the one time D&D tried, it pretty clearly went to hell in a handbasket.
It would take a fairly big adjustment to how people think of things, but one could in part define Charisma as being "strength of spirit/soul". Once you do this, then anything affecting the soul or spirit (most notably, death saves, which are another near-inevitability) would exclusively run through Charisma; as would revival from death if any uncertainty gets introduced there.
Well, I come from a context where there should be few to no bonuses to your death saves. But that's a separate concern. I do agree that this is an interesting direction to take Charisma, making it a very literal
force of personality/self. I could see this working, as you say it would primarily be a matter of selling the community on the concept. Unlike the Dex/Str issue above, though, I think this one really
could happen, though I'm not sure whether the design side or the persuade-folks-to-like-it side would be more difficult...both will be major challenges, at the very least.
Unfortunately,
@Maxperson is bang-on right: intimidation in real life works exactly as he says it does. Many (most?) of us have direct experience with this.
If the intent is for it to work differently in the game they should probably have put a different name to it.
I mean that's literally what I was saying. We need a new skill which covers more or less the ground Intimidate does, but also does other things, and
isn't the Evil Social Skill For Evil Evils Who Evil Evilly.