Yes, it is integrated with Google, in that it uses the Google API.
However, relevant to this thread, it's not developed by Google, as Thunderbird would not be. And so Thunderbird could still provide value as such a client.
I think this was the key. No average user I know uses an email client on their PC, outside of the corporate one. It's one more thing to take care of and average users rarely want that.
It's easier on mobile where people are used with the "app" concept, not really on the PC. This is one reason why Thunderbird doesn't enjoy the kind of popularity browser based email does.
Of course it's not impossible. But also they must be tech savvy enough to go look for an email client where they already had the usual web interface, get to testing a few and settle on Thunderbird, then configure and stick with it.
But that obviously it doesn't happen that often or else Thunderbird would boast a lot more users than it actually does. Relatively few users use it at all, and it's a reasonable assumption that the usage is higher among the more tech savvy than the average user.
I'm a fairly average user, in reality. One personal email address. Few rules. No integrations.
I still find it to be a significant improvement, even if most of my interactions involve arrow keys and the backspace key (ironically the keys I can't use in their web interface).