Imagine a Wizard. By 16th level, his initial Intelligence of 16 has been increased to 20 by stat increases, and another +6 from a magic item. At this point, we're talking about a +8 bonus to Intelligence skills. Meanwhile, his initial 10 Strength hasn't changed.
For comparison, here's that same character at 1st level. 10 Strength, 16 Int, no other stat boosts:
Ranking the combinations from lowest to highest:
Strength, untrained: +0
Strength, half-ranks: +2
Intelligence, untrained: +3
Strength, full-ranks: +4
Intelligence, half-ranks: +5
Strength, focused: +7
Intelligence, full-ranks: +7
Intelligence, focused: +10
Now, just to take it to an absurd extreme, depending on how much your players like to powergame, here's something that's not necessarily uncommon at 1st level...
A halfling (bard, ranger or rogue) with a 20 dexterity.
Hide: +16 (4 ranks, +5 Dex, +4 Race, +3 Skill Focus)
Even without Skill Focus you've got a +13 to Hide, and a Halfling Rogue with a 20 Dex is not especially uncommon even at 1st level.
Sure. But we are talking about skill checks where one guy can't get a success for the entire party.
Such as what...
Hide and Move Silently? Invisibility Sphere and Silence take care of that.
Balance, Climb or Jump? Levitation, Fly, Teleport, Spider Climb and Tenser's Floating Disk.
I can't honestly think of any other skills that fit that bill, other than Swim... And let's be honest, any adventurer who finds themselves swimming is in for trouble, whether their skilled at it or not.
That's the trouble... I understand what you're saying, I largely agree with the general idea of what you are saying, but in practical play for most players, it simply doesn't work that way.