For normal text. Headings and other content that needs to stand out should be sized relative to the main text, but why don't website (and ebook) publishers/designers leave the main body text as default, always? Why make users have to consider adjusting font size separately on every website they visit?
Fonts, too. Everyone has their favorite fonts, but the font a web designer likes has no bearing on what's best or easiest to read for the user. Are they developing a website as an art piece, or to publish articles for real people (not bots) to read?
Ancillary styling for text that needs to stand out, or text that isn't part of the main flow, can be whatever. But I don't even agree with shrinking footnotes anymore. There's no lack of page real estate at the bottom; there's no reason to shrink "back matter" except to imply that you don't expect anyone to ever read any of it (footnotes, index, bibliography, etc. in long-form blogs or books).