To put it bluntly.. I think this "just don't use it" meme needs to die. At this point in time, accessing certain websites is effectively a requirement of modern life: want to see your bills without paying for paper bills? want to apply for jobs? want to sign up for courses? submit your taxes? or even vote under some jurisdictions? Then you have to access a website. Sure, for a lot of these, there are alternatives. However, the costs will likely be much higher and you'll simply be left behind by everyone else in society.
This effort by Google, at its worst possible implementation, could break a huge number of "required" websites for users. As others have pointed out in this thread, the users who will be impeded are likely already at a disadvantage[1]. This just reinforces that, especially if everyone starts adopting this given how it is "free" for businesses/organizations.
A convenient side effect? Google gets more information about us and encourages us to view more ads.
[1] Someone mentioned smaller villages in India. The GOV.UK reference talks about users with disability. One could also imagine shared locations like public library, whose users may not have direct access to the internet.