The HTML 5 spec says exactly how you're supposed to deal with broken HTML files.
Yes, that is a single spec with correspondingly-small importance. Generally parsing html remains extremely difficult.
It's of quite large importance, and despite being difficult, it is well-specified, which is the point here. Importantly, there is also no competing HTML spec, either de facto or otherwise. CSV doesn't have anything of comparable authority.
> CSVs are the only "structured" format nobody can claim to parse 100%
You don't need to though since in most cases you just need to support whatever CSV format the tool you're handling, unless of course you're trying to write the next Excel/Google Sheets competitor.
My experience has indicated the exact opposite. CSVs are the only "structured" format nobody can claim to parse 100% (ok probably not true thinking about html etc, just take this as hyperbole.) Just use a well-specified format and save your brain-cells.
Occasionally, we must work with people who can only export to csv. This does not imply csv is a reasonable way to represent data compared to other options.