I don't think that this is Google doing the insisting but, rather, it is Apple insisting on using Safari to do the authentication to the Google web-authentication system. I believe a similar thing will happen if you set up a Microsoft hosted account through the "Internet Accounts" within "System Preferences" or if you need to authenticate your account to enable Microsoft Office. Setting up a Microsoft or Google hosted account within Outlook for Mac will also pop up an authentication window that might also be supplied by Safari, but my memory on that is hazy.Google Mail behaved oddly when I upgraded my MacBook Air to Mojave a few days ago. My default browser is Firefox, but Google insisted that I open Safari in order to set up my multiple Gmail accounts .... but Google insisted the setup had to be done through Safari.
Using Safari is not too unreasonable in my mind. Apple is confident that the software is installed on the system, and it is easier to test and audit a single setup rather than every possible browser that is available.