Monks are already MAD while wizards are SAD, and then there is the ever reviled dump stats. But instead of making classes sadder, and ending up with a bunch of characters who all seem to have only one or two functional ability scores, what if we went the other way?
First remove all semblances of weapon finesse and dex to damage feats and abilities (like dervish dance, fencing/slashing grace) and composite bows.
Instead we implement the rule that all attack rolls, melee, ranged, touch, ranged touch, use Dexterity + BAB
And damage rolls with melee weapons, bows, thrown weapons, and any other type of ranged weapon that relies on the wielder's own strength to propel its projectiles always add the strength modifier to damage. Crossbows still don't get anything but crossbows instead have a fixed damage that is higher than it currently is.
Now we do something similar for spellcasters. All spellcasting related numbers are still based on the regular spellcasting ability, except for spells per day.
-A learned spellcaster's (any Int or Wis based spellcaster) force of personality determines how much magic power they can focus each day and so spells per day are based on Charisma.
-Intuitive spellcasters (Cha based) however, who are surrounded by unchecked magic, must focus their minds to ration and gain more use out of their innate magic power. Divine spellcasters' spells per day are based on Wisdom and arcane spellcasters' on Intelligence.
-The exception to this are Paladins and Rangers, their magic is focussed on their roles as holy warriors and wilderness survivalists, so paladins gain spells per day based on Strength and rangers based on Dexterity.
To alleviate this need to spread ability scores more, Point buy gets more points per tier but any ability score above 16 becomes even more expensive.
So in the end there will be no more rogues too weak to stand, fighters who are too uncoordinated to take two steps without tripping over their own feet, and spellcasters have to make a more use of their full breadth of mental ability.
For the sake of this discussion let's ignore any non-core classes and focus only on core.
I would also prefer a system that is less rewarding for MAD builds and I have come to dislike all those options that allow characters to add ability 'x' instead of ability 'y' for the purpose of 'z'. They address the problem in the wrong way and are implausible from a flavor perspective.
One thing that I considered was using different mental ability scores for different schools/subschools of magic. I made some calculations how it would affect standard character builds, but I never got to working out all the details and writing it down.
When I reverse-engineered the point-buy of a high-level characters (including bonuses gained from level increase and magic items) and compared them for MAD and SAD characters, the result was unsurprisingly in favor of SADness, but the difference was not that big, considering the cost of raising a stat in the high 20s or 30s.
Two problems i'm seeing right now are
1: Monsters and pregen npcs are not adapted to this system, so if you were to implement it in the game, you would have to change them first.
2: Heavy armor needs changing, because with everyone having Dexterity it gets diminishing returns. One thing i can think of is raising all max dex bonuses or maybe even removing them entirely. But with attack bonuses probably flattening out slightly, that might end up with ACs generally being too high.
This actually hurts martials and gish classes way more than full spellcasters.
Combat builds generally have one of the following ability score foci:
A) High Strength and high Dexterity at the hefty expense of mental ability scores
B) High Strength with some Dexterity (usually going for heavy armor)
C) High Dexterity with some Strength
D) Full Dexterity (Dex-to-damage build)
Your suggestion effectively makes A and C mandatory while killing D and making B borderline non-viable. You also make melee builds less powerful because the advantage of doing a two-handed build is that you deal tons of damage and only need one ability score for your attack and damage rolls. Gish classes will also suffer heavily since A is not an option, you made B non-viable, and killed D. In addition, now a gish class needs two mental ability scores to cast spells instead of one.
Overall, this suggestion will hurt build diversity. It creates lots of problems while not really fixing anything. If you have to adjust point buy to offset the changes, then that just proves it doesn't accomplish anything.
Why would it hurt build diversity? It basically creates a situation where you have to find a compromise between accuracy and damage.
There is a spectrum between SADness and MADness. At each end of the spectrum, ability score allocation becomes meaningless (either because only one stat is important or because all stats are important). So the question is more about finding the right spot (right now, we are closer to the SADness-end of the spectrum). However, I think you have a point here: It would necessitate rebalancing the whole system on a larger scale (for example, the importance of Dexterity would need to be reduced in favor of other abilities--AC and Initiative would need to be influenced by another stat, Wisdom for example).
For what possible purpose?
Why would it hurt build diversity? It basically creates a situation where you have to find a compromise between accuracy and damage.
For many builds, this simply results in a character that is bad at both damage and accuracy. This makes those builds functionally non-viable at many tables.
If every martial character was nerfed evenly and monster AC and HP reduced to compensate then this might be fine, but different builds are affected very differently by these changes. Archery characters are no weaker (and, in fact, are a little bit better since they don't have to worry about strength rating), while melee builds suffer from reduced accuracy and damage. Some back of the napkin math suggests that a 1st level archery fighter has a higher DPR than a 1st level raging barbarian under your system and pulls further ahead at higher levels. Classes like the Bard and Magus, which now have 5 stats they need to invest in (strength, dexterity, constitution, intelligence, and charisma) are now so horrifically MAD that it's hard to see how you could successfully build one.
I believe a better approach is to use the carrot and not the stick. Look at the constitution score: it gives benefits that come up very frequently in practice. Hit points (and to a lesser degree fortitude saves) are always important, there's rarely a game session where they aren't. Dexterity and Wisdom, the other stats that are rarely dumped, also offer generally useful benefits that frequently come into play. Initiative and saving throws are a big deal no matter who you are or what you do. For many characters these stats are not needed at all for your primary abilities, but they still get investment due to the valuable secondary benefits they offer. This, in my view is the solution to the problem. Strength, Intelligence, and especially Charisma need bigger carrots to encourage investment, not bigger sticks to force investment.
In terms of the dex-to-damage issue devaluing strength, I've come across a surprisingly simple solution: a single feat that lets you add your dexterity in addition to your strength modifier to damage on any one-handed melee weapon. This prevents strength from being devalued, since even dex-to-damage builds still get a damage boost from it (or a damage penalty if they dump). It looks a little overpowered on paper, but in practice it's actually a great equalizer that has improved build diversity.
Why would it hurt build diversity? It basically creates a situation where you have to find a compromise between accuracy and damage.
The problem with that thinking is that accuracy is more important than damage. Part of the reason this is that most staple damage-enhancing abilities in the game already allow you to penalize your attack rolls in exchange for more damage. A character that prioritizes Strength over Dexterity is also a character that is less effective at using Power Attack, Deadly Aim, Rapid Shot, Two-Weapon Fighting, iterative attacks, etc. Also don't forget that Dexterity also has other very important uses, such as Acrobatics, dodge bonuses, Reflex saves, and initiative.
The OP's suggestion creates a game where Dexterity is always a combatant's primary ability score. That hurts build and character diversity.