You get a disconnect. You have a high brute strength, but when you hit someone with a club it has the same effect as that weedy guy you went to fighter school with.
Raw brute strength does not imply being able to use a club effectively in combat.
That "weedy" guy could easily have better training and battle instincts.
And this is not new to D&D. Go back to the very original D&D, and you'll find that a 3 STR Fighter is exactly as effective at killing goblins as an 18 STR Fighter. The higher STR Fighter only gains XP faster.
Even as late as 2E, a 6 STR and 15 STR character deal exactly the same amount of damage with a club.
You have a high dexterity, but you can't for the life of you avoid dart traps any better than the clumsy waitress.
Maybe you have really quick fingers, but not very fast at jumping out of the way. Maybe you are rather oblivious, and don't notice the trap until too late.
There are all sorts of ways a character could be good at Dexterity-based skills, but lousy at practical application of it in combat situations.
And again, in the original D&D, Dexterity had nothing to do with dodging things like traps. That was all about your class.
You have a high constitution, but when you and your unhealthy friend both ingest poison, you're no better at coping with it.
The long-term effects of poisons would reasonably be the domain of Skills.
But I think it's entirely reasonable that, for the short duration of a combat, the training and battle-readiness of the combatant could mean more than pure healthiness.
Either you accept that abilities in some way represent your natural (or trained perhaps) talent at things, or they don't. Should you smash up an altar more effectively because you're strong? Then why can't you smash up a golem better? Or a goblin?
But why should "smashes altar effectively" necessarily imply "smashes goblin effectively"? They are very different targets. Smashing an altar is a pure expression of strength. Hitting a goblin effectively involves varying degrees of accuracy, force, tactics and perception.
And not tying Strength to Fighting ability mechanically doesn't mean that you can't, within the story, tie them together. A player can easily say that a lot of his Fighter's talent comes from his brute strength. But another player could say that his Fighter mastered an ability for pin-pointing strikes through accuracy or tactics.