They don't fight on an even basis when those who just dump their mental/social stats get to have extra physical stats. I'm firmly in the camp of Play your stats. You the player might give a well reasoned argument. Your low intelligent/charisma character doesnt. The lack of decent social rules in D&D shouldnt be an excuse to dump them even further.
I am not really picturing where you think the imbalance is going to actually show up. Depending on the class dump statting dex or strength works too so it seems to not favor the way you are implying.
Can you give an example of where you think the imbalance would work out with the 15/15/15/8/8/8 array?
A heavy armor cleric can dump stat dexterity, intelligence, and charisma.
A fighter can dump stat charisma, intelligence, and dexterity if he goes classic heavy weapons.
A sorcerer can dump stat strength, intelligence, and charisma.
A wizard can dump stat strength, wisdom, and charisma.
A warlock can dump stat strength, intelligence, and wisdom.
A rogue can dump stat their choices of strength, intelligence, wisdom, or charisma and make it work.
All of these seem straightforward optimization and seem balanced against each other for combat.
The classes that could be behind the curve are the MAD ones, a melee valor bard for instance can dump stat intelligence and Charisma but would be hit hard by the third dump stat.
A non-heavy armor cleric is hurt hard if they dump stat dex, dumping strength is an option for a more caster focused build.
If you only go with one dump stat - say the standard array - then anybody but the wizard and some specific subclasses can dump int. Anybody but charisma classes can dump stat charisma. Anybody who does not use strength for armor and attacking can dump str.
Otherwise SAD casters become the best roleplay and combat options having a class stat for combat power doing double duty as either social or cunning.
Everybody else has to divert a lot more away from their MAD requirements for baseline combat power to add in the one or two roleplay stats. And the MAD classes that don't depend on charisma or intelligence at all are the worst.
Robert Downey Jr. Sherlock the excellent bare-knucle brawler monk investigator concept is therefore going to be the most spread thin stats build in the game watering down the monk combat for the roleplay if you want to also hit the roleplay thinking and banter aspects. High charisma and intelligence Warlock/Sorcerer/Wizard RDJ Sherlock is fairly trivial to pull off at full class combat powers to get both the roleplay witty banter and the logic, although at the cost of really crappy punching combat with the spellslinger build.