Simply put, mental stats do have relations to and interplay with the physical stats, but it's not quite as heavy as the physical stat's interplay with eachother.
Also D&D stats are not sufficient to represent human ability. There's a lot that weirdly stuffed together, or just plain missing. And Charisma isn't a stat. It's a skill, yes modified by one's intrinsic beauty, but not universally, and there's diminishing returns. A more accurate and useful stat breakdown is as follows (though it's more to keep track of)
Physical:
Strength (Muscle power, affects how much weight one can move and with what force. Think momentum, inertia. Think a boulder, rolling slowly. It's not fast, but it's hard to stop)
Agility (Quick muscle movement, affects how fast one can move the weight determined by strength. Does affect damage by virtue of how kinetic energy works, but strength is still important too. Optionally, also includes reaction time)
Dexterity (Precision of movement, and flexiblity. Useful for heavily skill-based tasks, like sword fighting, dancing, playing instruments, crafting)
Resistance/Constitution (Basically, durability, resistance of the body to damage)
Vitality (More optional, this affects healing rate and hp if such a thing exists)
Stamina/Endurance (How long one can exert effort, and rate of recovery of stamina)
Mental (you can have this overlap with magic, or let magic be it's own thing)
Processing (Quantity of information that can be processed at once) (Affects useable spells, allows bigger spells to be cast easier, essentially increasing their power)
Intelligence/Acuity (Speed of thought/information processing, could mean agility doesn't affect reaction time) (Casting speed)
Focus (Attention to detail) (Precision of casting and minute control/modification of spells)
Willpower/Discipline (Ability to push through, be that exhaustion, pain, or mind-effects) (Maintain control of spells despite interference)
Wisdom (Retention of information and recall ability) (Mana pool/regen)
And then kinda sitting on it's own,
Perception (Kinda optional, Processing, Intelligence/Acuity, and Focus all can kinda combine and take the role, with special abilities for more esoteric types of perception)
There's a lot of inherent interplay in the human traits, especially physical. Strength doesn't mean speed, a fighter needs both because speed contributes to damage majorly as well (and to hit targets), pure strength might be something used by a common laborer. And if you have high speed, you'll need comparably high dexterity to maintain control over it, and probably Acuity at higher levels to be able to keep up with yourself. And the inverse, people with high acuity might find their minds moving faster than their bodies and seek agility for balance. Those with high strength need decent constitution or their strength can damage their own body with the strain.
A fighter will probably also want good focus to read their opponent, processing becomes more important against multiple opponents or in tough terrain, willpower to maintain focus despite wounds and/or exhaustion. Even wisdom, because that will help with learning faster.
Every stat is essential to a fighter in different ways. Spellcasters can get away with skimping on physical stats, but should probably have a decent Constitution and Vitality to endure their own magic, and Agility to keep out of fights. Laborers and farmers can skimp on mental stats, certain craftspeople might not need more than a certain level of strength, etc, specialty jobs can get away with skimping in some areas, but most people will probably want at least a bit in every stat.
Dexterity (Precision of movement, and flexiblity. Useful for heavily skill-based tasks, like sword fighting, dancing, playing instruments, crafting)
Focus (Attention to detail) (Precision of casting and minute control/modification of spells)
Thinking on it, it might make more sense to take Flexibility out of Dexterity and make it it's own thing, and similarly with Focus extract Adaptability or somesuch for adapting to new surprises and unfamiliar situations, as well as modifying spells or using them flexibly. Adaptability would then counterbalance focus to help against getting stuck in one mindset or focusing on one thing and not catching other things.