I think we need to be careful with the words censure and erase.
Google is a company and has no obligation to index any sites.
As consumers we can visit any sites we want on the internet. Google is unable to prevent us from doing so. That’s nothing like China literally blocking sites from everyone’s access.
So google is free to include whatever sites they like in their indexing. They have a financial interest to be perceived as “objective” and include all sites, not a legal obligation.
And we consumers are free to use whatever search engines we want.
If Google were ever declared a monopoly they could lose some of their freedom to choose.
You make some good points, however, we already know that Google leans to the left. So we already know what kind of erasing they are going to do.