I've played through a variety of different RPGs, and Strength and Agility almost always remain independent short of ultra-minimalist games that have 1 stat for everything physical and 1 stat for everything mental. Those games usually reinforce concepts with skills, ie: lifting and tumbling are different skills, so the "buff" characters have more "strong-man" skills and the "agile" characters have more dexterity-related skills.

5E doesn't have enough skills to do the latter. But D&D has never really had enough skills per stat to truly bring a character to life based solely on their skill selection.

Which is part of the problem with some stats and not with others. They have fairly low representation in the game. Dex has fairly high representation in the game. It has a couple skills, it covers a couple tools, it applies to some important secondary stats, it covers a couple modes of combat.

Strength...does not. It covers a couple modes of combat (default hitting and grappling), a one skill (although optionally any skill in 5E can be paired up with any stat if the DM chooses), lifting/carrying capacity (arguably something that doesn't come up in play often) and a couple tools (though again, tools don't necessarily have a default associated stat).

Con has a similar problem. It doesn't cover any modes of combat. It has no skills (although the DM may call for Con checks in certain situations). It doesn't really have any tools*. It helps HP.

Int is well represented in skills, with 5 of them, covers a mode of combat (spellcasting), covers some tools*,.
Wis is well represented in skills, with 5 of them, covers a mode of combat (spellcasting) and again, covers some tools*.
Cha, again, is well represented in skills with 4 of them, covers a mode of combat (spellcasting) and again, covers some tools*.

Ideally, all stats should look like the mental stats. 3-5 skills, covers a mode of combat, covers some tools and applies to one secondary area of the game(AC/HP, etc...) (the mental scores mostly lack this).
*Again, tools can in theory call for any base stat or paired skill.

Strength needs a buff as does Con, together they'd about even out. Dex doesn't need any buffing or to cover any additional elements of the game. While I agree that a player can simply choose to "not" make rolls they feel are inappropriate to their character's concept, there certainly is a high pressure in D&D to "roll for it anyway" if you've got a good stat in it (something I dislike about the game).