I'm not sure that something like HTTP 1.1 is hard to implement. There are miriads of HTTP servers and clients. It has its quirks, for sure, but you can code basic implementation pretty easily.

Now rendering HTML is completely another level of difficulty.

If you ask me, I'd suggest to use Markdown instead of HTML for "simple web", but keep HTTP/1.1. Rendering Markdown is relatively simple and it's rich enough for a lot of document-based websites.

As for "web apps": use webassembly as underlying execution engine, but build something new for rendering, not coupled with any markup languages. Just provide canvas to draw and efficient API to implement draw operations. Application developers will use frameworks and frameworks prefer to draw everything themselves anyway. I think that kind of "web app engine" would be possible to implement with limited development resources, unlike modern web browser.