Humans are adaptable, versatile, ambitious (due to the shorter life span than most demihumans), and I'll throw in what someone said about capable of learning well.
Humans, or MOST humans, should not be as agile or generally as wise as an elf, hardy as a dwarf, strong as a half-orc, or as "lucky" or nimble as a halfling.
Humans ARE the default (if you want to make a non-humanocentric world, go for it, but the game has to start somewhere).
I say the +1 across the board doesn't really make sense...while making sense. If humans are the baseline that elves, dwarves, etc. receive a +1 to their specific areas then it doesn't really make sense...you're just taking the baseline and adding 1 to it across the board...so there IS no "baseline" there's only "baseline +1."
I do get the argument that adventuring PCs are just "better" than your normal commoner human, that makes sense to a degree...but I don't think it necessary to give them +1 across the board to accomplish that. Part of the fun of roleplaying is figuring out and playing to your strengths and weaknesses. Giving everyone +1 to everything just seems like you'll end up with every human PC, and classed NPC, being rather "the same" as each other and generally 'better" than all other races. Everyone is fairly as strong, as smart, as charismatic...within a couple of points of each other...and I'd rather see the strong but slow/dim fighters and the charismatic but clumsy rogues, or the dextrous but addle-brained wizards in the mix as well.
If they ARE going to go with +1 across the board than there is certainly NO reason for a floating +1 on top of that!
I would say, better, give humans floating +2 to ability scores. So if you want a Conan-esque fighter, put +2 in your Strength. If you want some streetsmart quick moving thief, put +1 in Int. and +1 in Dex. Yes, you/this particular human MAY be just as fast or smart as an elf or as tough as a dwarf, but not every human should be able to have a Con. as good as if not better than a dwarf, etc.
This will also allow the bonuses toward certain (not ALL) saves/checks in abilities where the floating bonus(es) are applied.
Add to that, for the versatility/learning thing +1 skill of choice, regardless of background, for something they "picked up along the way." Maybe 2 skills...so it would be like a "half-background"...something they were exposed to/around, but didn't really ever "study or train fully in.
So, +2 floating applied to ability scores (and thus to the checks/saves of those abilities), and extra skill(s), and that's all.
That makes the humans "feel" human to me without all being supermen. They get to apply +s to their character sheets too, but only a couple (not 7!), so the Balance-meisters don't get all in a bunch. And a couple of extra skills to offset demihuman special abilities.
That's what I think/my 2 coppers, anyway.
--SD