If you really want HTML, well, SVG has the <foreignObject> tag which you can use to embed HTML (in the XML serialisation, so for once you will need to write <br/> instead of <br>). But pure SVG is likely to be a better idea.
Sample markup to drop in an HTML file to get an HTML-powered “Hello, world!” favicon:
<link rel=icon href='data:image/svg+xml,<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 48 48"><foreignObject width="48" height="48"><div xmlns="http://www.w3.org/1999/xhtml">Hello,<br/>world!</div></foreignObject></svg>'>SVG can include foreign objects, which is decidedly useful in some contexts; in browsers, that includes HTML, because it’s easy.
A favicon is an image, so it should allow all the usual types of images, which includes SVG. No reason to exclude SVG or any SVG features other than scripting.
(“But now a non-browser can’t render the favicon properly!” you may say. By using <foreignObject>, you’re opting into non-standard functionality and shouldn’t expect all SVG renderers to be able to render that part. For completeness, I’ll note that you can provide an alternative representation for engines that don’t support XHTML in SVG with <switch> and requiredExtensions.)
I personally don't see a good reason not to render server side and save page load time, batteries, cpu cycles, etc.
It's definitely a natural consequence of constant improvement of the tech, but I don't like each step piles on technical bloat.
Yes, CPUs and browsers get faster over time, but all those improvements usually lead to more software bloat and cancel each other out. Which is a shame really.
A majority of people in the world use old, non updated phones to access basic websites. Improvements like this can lock people out of portions of the web just because their browser can't handle rendering the favicon.