The 6 attributes are the most sacred of the D&D legacy elements. But what if we just eliminated them entirely? What if we just used skills, proficiencies, feats, etc to define what a character is good at mechanically?
Could D&D be D&D without ability scores? Would you play D&D without ability scores?
Well there are such games which work. Beacon comes to mind (it does have stats but they are different from ability scores (only affect defenses) and also they would not be necessarily.
However, leaving them away does lead to some problems.
Ability scores do tie together combat and non combat in a really simple manner. Beacon, Lamcer and other games which dont have them, often have combat feel completly separated from the non combat part. Sometimes even like its 2 different characters. While a spellcaster using charisma for casting also feels charismatic in non combat. And a brute force barbarian who hit things hard, is also good at using the brute force to open doors.
Then they also do tie together abilities in a coherent way. Skills in real life also have some links together. People who are good at swimming and biking most likely are also not that bad at running.
Endurance, strength, speed and flexibility are real life stats which are measured in "sport tests". Similar "intelligence" does have a measurable effect to many difference things, similar good look does have a positive effect (provable) in your life in different aspects.
Of course training still does also matter, but having some mechanic to tie connected things together helps to make the feel more coherent and also allows you to do get better at things without needing a specific mechanism for that 1 thing.
Then having attributes can also just be a "natural" (or more natural) way of progress. After several levels of training your strength increases and thus you are stronger in combat feels a bit less unnatural than "ok your proficiency (with everything) now increases by 1".
Of course there are way around all these things, but they often are more complex and require more work. Also getting rid of othet things lile 15+ skills, gets rid of a lot more space/complexity than getting rid of 6 attribute scores, while losing less.
Some way around these limitations:
- Using skill powers like D&D 4e did, can tie skills used mainly out of combat together with combst abilities
- Having you get new/stronger attacks like in Gloomhaven (new card each levelup) also feels like a natural poeer increase without needing stats.
- Using backgrounds like 13th age instead of skills also tie together thematically abilities fitting together
- Designing classes with both in combat and out of combst in mind and having abilities for combat mirroring abilities for non combat can help. Like giving characters which out of combat can break doors easily combat abilities which can kick enemies away etc.

