This is interesting. The argument which I’m gleaning from the essay is that the old proposed API of having an intermediary new Sanitizer() class with a sanitize(input) method which returns a string is actually insecure because of mutated XSS (MXSS) bugs.
The theory is that the parse->serialize->parse round-trip is not idempotent and that sanitization is element context-dependent, so having a pure string->string function opens a new class of vulnerabilities. Having a stateful setHTML() function defined on elements means the HTML context-specific rules for tables, SVG, MathML etc. are baked in, and eliminates double-parsing errors.
Are MXSS errors actually that common?