> the server sends the HTML already built and the client just places it where it belongs

Mind blown.

A much bigger pet peeve of mine is making a SPA when a bunch of HTML pages would do, and would give you sensible URLs and the ability to open more than one tab in the first place.

When you actually need a SPA, I'd only go websockets if I really need that low latency and your clients are close enough in the first place, if they're half the way around the world on a slow connection you have different design constraints. A chat application works just fine over SSE or similar. Client-initiated requests even work with plain old fetch().