When I share a google doc, it’s not only over a email service of the same vendor, it’s just a link I can send anywhere.
Well you’re sending a link to a Google hosted service. The other side necessarily needs to interact with a Google service in order to make sense of that link, and, if they so choose, make edits directly in that Google service or export with Google’s export functionality. If you send that link, a Microsoft Office user won’t simply be able to open it in Microsoft Word (and even if Microsoft implements that functionality it would require Microsoft to actively maintain an API key with the Google service).
If you’re sharing a calendar entry between the current big 3 (Microsoft Outlook, Google Calendar, Apple Calendar), it sends an email to the other. From the users perspective, a Google user never has to interact with Apple’s servers, or a Microsoft server (whether a local Exchange server or a cloud-based 365 one), because everything necessary comes to that users own server through a federated messaging service (email). You just send an invite to user@domain and it just works, but the protocols all simply assume that user@domain is an email address and that sending email to that address will cause the other user’s email service to process and process that calendar invite for that user.
It’s 3^n, not n^3. n^3 is actually way slower.