I hear this argument a lot, Americans insinuating their different states are effectively almost different countries.

It is nonsense. Americans are Americans. Of course you have regional differences, no different to people from York and Bristol would. But you're not as diverse as you think.

Outwardly I'm sure Brits, Australians, Chinese, Indians etc all get lumped together in your head, despite each of those countries having extremely differing internal cultures spread across the respective countries. That's how the rest of us see Americans - LA and New Yorkers are not different, except in subtle ways only obvious to you.