Then why do you want strength to have an effect on your ability to break down doors?
Because that would be the specific point of having the Strength ability exist. To use for skill rolls where strength is the dominant force. That would be the role of the mechanic.
Same reason we have attack bonuses for rolling to-hit, and damage bonuses for adding to damage rolls. That's what those mechanics are there for.
The weedy guy might be an expert in carpentry.
Then the weedy guy would probably have a skill of some sort for carpentry, and the DM could allow him to apply it, if the DM felt is was relevant.
You either accept that both skill and talent play a role in both combat and other activities
I absolutely accept that.
I just don't think it's necessary to mechanically model skill and talent separately in all cases, and for talent at non-combat tasks to necessarily be the same as talent for combat tasks.
or you do away with ability scores - that's a different game altogether.
Not necessary. Ability scores are a perfectly fine mechanic for making skill rolls.
For 2E though, note that they decided that very weak and very strong characters should deal more damage? There's an ability component and a skill component (weapon specialization).
Yes, they do express it mechanically as ability component and skill component. But it's hardly
necessary to split out ability and skill mechanically for it to make sense in the fiction of the world. If the mechanics only say what the net result is, and not, specifically, how it's arrived at through ability and skill, what's wrong with that? Why can't one player say "my fighter is awesome because he's super strong" and another say "my fighter is awesome because he has exceptional training", and have them arrive at the same place in terms of combat effectiveness, without needing to jump through mechanics hoops like "Weapon Finesse"-style feats and/or specific weapon choices? What's wrong with writing "Fighter" on your sheet, and letting that establish that, yes, you are indeed good at fighting?
But my point was, with 2E, given that is 6 and 15 being equivalent for damage, is it really such a stretch for Next to have 10 and 18 be equivalent for Fighters, in terms of their combat effectiveness? Is it really the case that 6 being just as effective as 15 is true to DnD, but 10 being as effective 18 (or even 16 being as effective as 18) is not?
Well what I take from that is that maybe we should use dexterity and strength together to see how effective you are at hitting goblins (I think this has been done somwhere?).
But that's needlessly complicated. There's no need to go through all of that just to arrive at a to-hit number.
You're right that smashing an altar is a pure expression of brute strength, but then taking the extreme position that hitting a goblin is a pure expression of skill - that it doesn't matter how strong you are, you'll hit it with a force based on how much sword-fighting you've done, and you'll hit accurately for the same reason, ignoring that you're naturally dextrous.
Having accuracy be based on class does not imply that, in the fiction of the world, strength and dexterity don't matter. It's just that their effect is included, if the player wants, with the abilities gained from class and specialization. Or they could say that their Fighter gets most of their effectiveness from superior tactics or situational awareness.