"even if somehow server-side algorithms are better (which this presentation seems to imply)" The slides provide several reasons why server-side algorithms are

"even if somehow server-side algorithms are better (which this presentation seems to imply)" The slides provide several reasons why server-side algorithms are worse. "the situation is better client-side, because when running code on the client's side, you can check how exactly the browser parses the HTML code." Yes, and for this reason, DOMPurify is a client-side sanitizer.