Inline HTML is part of the standard Markdown syntax, not a complication. If your tool doesn't support HTML it doesn't support Markdown. The format can be so simple in the first place because it allows this escape hatch for anything non-trivial.
And tools like Pandoc can handle that just fine.
My point is that Markdown conversion tools, notably Pandoc, whilst they will incorporate inline HTML when generating HTML endpoints will not convert such inlined code to other endpoints, e.g., LaTeX, DocBook, OpenDocument, etc.
If you want those outputs to faithfully represent formatting, you either need to juggle multiple inline directives for each desired output format, or find some universal Markdown-based mechanism for achieving the same result.
I'd like to make clear that I'm familiar with Markdown; the fact that its original design intent was streamlining HTML generation; that inline "native" code is a feature, not a but, but all the same a rather fraught one; and that actual practice has moved far beyond Markdown merely being used to generate HTML, least of all my own such practice.
I've discussed this situation previously on HN (ironically from the PoV of using LaTeX embeds within Markdown creating problems when attempting to generate other-than-LaTeX outputs), see: <https://news.ycombinator.com/item?id=29690056> (2021).