Originally, this was the case, but I'd argue that modern MarkDown flavors have been separated from HTML. It's common to compile via other pathways than HTML now (e.g. MarkDown → LaTeX → PDF), and many implementations don't support inline HTML anymore (e.g. many MarkDown-based note-taking apps).
> I find that perfectly normal documents need to write raw HTML regularly, because Markdown is so terribly limited
Out of curiosity, what do you need it for? I write a lot of MarkDown, but haven't felt any need for writing raw HTML. Modern versions of MarkDown (e.g. the Pandoc variant) have native support for things like tables, LaTeX equations, syntax-highlighted code, even bibliography management.