I'd argue that there is a very strong value in doing something good, not just because it's genetically or socially imprinted on you, but because you actually decide to do it.
This applies to everything, there is no merit in being good at something just because you were born that way.
I would posit that no, it is not. And it's not even unambiguously a good thing. There are plenty of cultures where people are described as cold until you get to know them, but once you do - they'd die for you. To me, that is genuine care. The American "Hiii! How ARE you? I don't actually care if you keel over and die!" approach feels fake.
No one in this thread is talking about your example except for you, and it would perhaps do you well to reflect on why you read things that way.
Brits offer, "Cheers!", but don't actually invest in hoping you feel cheer.
Chinese say, "You good?", to which one replies, "Good." Same thing as Americans.
Etc. Greetings the world-round are typically a surface-level check on well-being, without a huge emotional investment.