I think it would be more like "You can't use Free App Engine and infra without giving Google a cut".
Now if you can't access the app at all, such as by browser or etc, then i think there's a better parallel to Chrome. But when you're using someone elses infra entirely it feels odd to say you have the right to use it for free.
The donations aren't the problem in my mind. Installing applications outside of the app store is the problem. Because locking app installs down and not supporting alternatives like PWAs is the real devil.
I still partially think we should just avoid Google phones period, but other comments suggest Microsoft already was forced to allow alternate browser installs, so there in i think that sets a precedent to require Google/etc to better support 3rd party app installs (out of store).