IMO. Most of the problems you cite with modern D&D stem from a few areas
1. Trying to be too granular.
Granularity allows for customization. It makes many different kinds of flavor possible. It is part of why the D&D 5e gaming system can be used for so many different genres.
(To be fair, every genre needs to be a flavor of combat. But even then, it is possible to play D&D without combat.)
The difference in a single attribute bonus barely matters in actual play.
Optimizers care deeply about a single bonus from an ability. Their various builds speak for themselves about the mathematical usefulness of an ability bonus.
In normal play, there is a feeling that the +1 of a d20 is (coincidentally) the right amount of difference. Indeed, if an option only grants a single +1, players take it or leave it. But if an option is +2, it becomes a must-have. For example, switching to percentile d100 dice would not meaningfully improve the game, in the sense that the difference between +001 and +002 would be mostly a meaningless waste of time.
Relatedly, I feel strongly, that if I had to choose between +2 and Advantage, I would pick Advantage. But if I had to choose between +3 and Advantage, I would definitely pick the +3. (Advantage is good, but becomes less good when one really needs it to succeed at something difficult. Then the flat bonus is significantly more helpful.) The fact that the differences between +1, +2, and +3 can 'feel' different from each other, confirms that this is a useful and meaningful amount of math.
A single ability bonus matters.
2. Grouping specific skills to attributes (and really having that split between skills and attributes at all).
It's part of the reason a really intimidating Wizard is so hard to make in D&D.
When I DM, I rely on the abilities. Something requires strength-toughness, mobility-precision, social-skills-self-expression, or other kinds of knowledgeability-awareness. It is normally obvious which ability is relevant for a given challenge.
The skills are more fluid, as a thematic 'proficiency' bonus, and might circumstantially be relevant for various kinds of ability challenges.
Note, the abilities dont need to have the same number of skills. Constitution has the trait of Hit Points, and while it is its own problematic, it is effective enough without combat skills.
3. Current system design makes dex, con and class main stat the primary combat stats and everything else if for out of combat.
Yes, D&D 5e overuses Str, Dex, (Athletics), and Con for combat, and underuses Int, (Perception), Cha, and Wis.
Blame 1e.
1e evolved from a wargame. It had a divorce between highly regimented mechanics for physical combat. And almost zero mechanics for mental challenges in noncombat scenarios, where players themselves would come up with the solutions. The mental abilities on the character sheet were large irrelevant to actual gameplay.
The only time mental abilities came up mechanically was for spellcasting stats in combat.
D&D has evolved much since. Mainly 3e made the breakthrus for standardizing and quantifying uses for the mental abilities. 4e made any ability equally useful in combat. (For example, one can use either Dex or Int for the Reflex Save.)
5e is now in a situation of wanting to keep the abilities thematically distinct, but overall equally useful in combat.
This is fine except leveling in D&D typically come from defeating enemies and failure in D&D mainly stems primarily from dying in combat and so the combat stats are already inherently more important. If TPK's potentially depended on passing animal handling and medicine checks, then those would be top skills. If we had alternate paths relying on insight/intimidation/etc to defeat every enemy in the game and protect us from potential TPK then those skills would be just as valued.
Totally agree.
While it is possible to play D&D without combat, this game evolved from a combat game and remains combat-centric.
Heh, probably the greatest challenge today for D&D is how to be a combat game and at the same time sound "ethical" during the roleplay aspects of it. Most of the game can sound kinda murderous.
Regarding the abilities, it is easy for the mental abilities to be as important in combat as the physical abilities, even tho 1e didnt do this.
4. The magic system
Magic does too much independent of everything but main stat (or i should say only dependent on class).
I do too (well not the classless system). But Balance does not equate to 'no dump stats'. Those are 2 separate desires.
Regarding dump abilities. Once an Attack ability is chosen, the other Attack abilities can be dumped. However the Save-Utility abilties are always nice, often necessary, and painful to dump.
Part of the reason for the current situation where the casters a Single-Ability-Dependent for casting:
Example. The Wizard is Multi-Ability-Dependent. It must have high enough scores in Intelligence (for casting), Dexterity (for avoiding getting hit and surviving most spell attacks), and Constitution (for surviving combat generally).
If instead, all of the mental abilities were useful for surviving and winning in combat, then the Wizard would be less dependent on the physical abilities in combat.
Then, the mental abilities could also relate to different aspects of spellcasting, analogous to how the physical abilities relate to different aspects of physical combat.
It's not so much that such a game would be Atonal, but it would just be missing a wide swath of potential tones. But again, the concept was a starting point to get to a particular place, not a stand alone example of a finalized game design.
If there are only four classes, it is virtually the same thing as having only four abilities, except player customization becomes impossible, and the DM has a more difficult time running it.