That's why it is better to have both.
Nope. It's more samey, not better.
Nope, try again.
No. I'm just saying that every barbarian halfling will be that bizarrely and uniquely super strong one.
And again, you are not going to have "every" barbarian halfling in your game, so it won't actually affect you at all.
And let's say that you actually manage to play with multiple super-strong halflings over the course of your gaming life. So what? How does that
actually affect you? Is it actually worse than every halfling being a rogue, or every orc being a fighter, or every dwarf being a drunken pseudo-Scot? Would you refuse to play with people who don't make totally unique characters?
Right. I understand this. What I do not understand why you consider this to be acceptable. Why it is unacceptable for ASI's to make certain races suboptimal for certain classes but it is perfectly fine for the traits to do the same?
Stats are already individual. Each player has a different set of stats.
Racial traits aren't individual. And since this isn't a game like GURPS, racial traits will stay unique to the race, not the individual.
Under PHB rules you couldn't. And that makes certain sense to me. You can be abnormally weak orc. And that orc will have strength this. This is perfect representation of the strength of the orc species. Even a feeble orc is as strong as an average human. Same with clumsy elves. They have dex ten and are as agile than average human. But from elven perspective that's terrible.
If 10 is average, then the average human has an 11 in all stats (+1 to all stats, remember?). The average elf is only a tiny bit more agile than the average human. The average orc is only a tiny bit stronger than the average human. The average halfling is only a tiny bit weaker than the average human--but is exactly as strong as a loxodon, despite the fact that the average loxodon is 4-5 feet taller than the average halfling and can lift one in its trunk. Halflings are also exactly as strong as hobgoblins are, even though hobs are specced for war.
And the average human is exactly as strong as the average firbolg or leonin--even though one is basically a short giant and the other is an anthro lion, and both stand a foot or more taller than the average human. And the average high or wood elf is exactly as smart and wise as a human, despite being likely a century older. The average githyanki is as strong as a goliath, despite being quite a bit shorter and being described as slender.
This is one of the problems with ASIs: they make no sense. A perfect representation of an 8-foot-tall anthro elephant is exactly as strong as a 3-foot-tall furry-footed halfling.
You have a problem with strong but small halfling barbarians. Do you have a problem with the idea of a strong anthro elephant barbarian? Or a strong tiefling barbarian? Or a strong leonin barbarian? Or a strong hobgoblin barbarian? Or a strong lizardfolk barbarian? If so, why? And if so, why should everyone else have the same problem you do?
And, why should I be forced to play a "perfect representation" of any race?