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Right now a 1st level character can only put 1 rank into a skill. Sure, she gets the +3 if it's a class skill, but the fact remains that she can only have 1 rank, which means all 1st level characters have the same degree of skillfulness.
[Okay, that's a bit of hyperbole - they can end up with +0, +1 or +4 - but they really do all end up with the same 1 rank.]
If we bumped the max ranks by just 1, to level+1, you'd have some characters who continue to spread their points and by 1 rank in each skill. But you could also have some characters who invest 2 ranks in a smaller number of skills. End result - some 1st-level characters that are 1-ranks good at things and some that are 2-ranks good. Variation, which, to me, is good.
It shouldn't imbalance things because they could be better at things but not as many things. They'd actually miss out on some of the +3 class bonuses by taking fewer skills (they'd probably pick it up later though). By 20th level, you'd end up with some 21 ranks, effectively +24 in class skills, but that's only 1 point higher than now and some other skill would be 1 point lower.
This wouldn't affect backwards compatibility at all because the current max rank = level cap simulates 3.5 just fine. If Pathfinder went with max ranks = level+1, all those characters would still be possible; it would just be as if every character and NPC up until now put 1 rank into each of their skills. A new character could be slightly more proficient with a skill that a 3.5 character, but she'd have to be less diversified.
While I like the idea, there is but one problem that you already mentioned by the side.
Characters end up with effective rank = level+1 or level+4 (class skill).
So they get all ranks one level earlier than under 3.5
This will have (I won't say a major) effect on Prestige Classes.
So the easy way would be to reduce the class skill bonus by 2, but this would bring class and cc-skills even closer, and I don't know if this is the way we wanna go.