I get the motives behind the "indie web" movement, but I really don't think everyone needs a website.
Just look at the websites hosted on any free web hosting service, both old and new. That vast majority of them are almost empty with messages saying "coming soon" and they tend to stay that way forever, or they just give out a few facts about themselves a blog with only a few posts, and that's it. People don't realize that that's what basically killed GeoCities and other free web hosts. Unless you have something really interesting to share, there is no point in having a personal website. The personal websites you loved to browse back in the day (and maybe now) were the diamonds in the rough.
I do agree that artists, indie game studios, small businesses, non-profits, self-employed entrepreneur's, celebrities, activists, etc should have a website and focus on that rather than social media, but to say that EVERYONE needs a personal website is a bit of a stretch.