I don't know about this weakening of the .270's 'greatness' that people have observed.
Its in the top five hunting cartridges in the world. Right now. It's as popular in Europe Aus and NZ as it is in America. It's been that way for decades.
I would argue that popularity over ninety years is definitely a measure of "greatness". (There's not too many people around calling the Sharps .44-77 a "great" cartridge.)

No one I know thinks of the .270 as an "American" cartridge - its just the .270. A standard caliber for everyman, and considered quite a powerful number. It's so accepted and normal that no one talks about it. (By contrast (In NZ) the .30/06 is considered an "American" cartridge, and is not very popular at all; people think it kicks too much)

If anything the .270 is in danger of falling out of fashion because its so boringly efficient that its "old hat" to the younger crowd who are bent on shooting the 6x47mm and the 6.5 Creedmore and suchlike at long distances.

But the idea that it is falling out of favour because of non-performance on game....

Can you imagine a modern rifle manufacturer bringing out a new model and NOT chambering it is .270 Winchester?