I pulled that example straight from the PH.
Well, that's just dumb. Strength only matters when chopping wood. If you are making a cabinet or a chair, dexterity or intelligence would be much more appropriate. In 3rd edition crafting skills (like carpentry) were Int based. But that's neither here nor there. If you think it makes sense for brute strength to be the primary ability required for building a cabinet or a house, then go with it. (I'm going with the 'designers didn't really care enough about carpentry to think it through'.)
That example was to counter your earlier claim that it's only a problem when you have an 8. Clearly that's not the case.
I don't think you understand the meaning of the word "clearly". It's not clear at all, or we wouldn't be debating the point.
Now you're saying that a +1 bonus doesn't matter, which is an odd argument in a game built on small bonuses.
It's the smallest possible difference in skill you can have. If you are going to get this wound up about a +1 difference in a non-combat situation, then I think we are done. The game just isn't as granular as you want it to be. House rule to your hearts content, because "clearly" this is particular issue much more important to you than it is to me.
I do want to note that I'm not saying there should be no difference between someone proficient with a tool/skill and someone who isn't. I'm just saying that the differences for most adventuring purposes are negligible. The non-proficient person picking the lock probably makes more noise and leaves obvious scratches on the lock, and it may take longer (depending on the DM - I would make it take longer) - but the end result would still be same. The lock would be picked.
The non-proficient carpenter may make a stool that looks ugly, with rough edges and a few irregularly shaped bits, but they will still end up with a thing with 4 legs and a seat that can support their weight.
The game simulates killing monsters and taking their stuff, it's not so good at simulating everyday life activities. It's just too abstracted.