Currently RemexDriver does not implement validate(), so MWTidy:checkErrors() throws an exception. The function is used in MediaWikiTestCase::assertValidHtmlDocument() and OutputHandler (if $wgValidateAllHtml = true;).
It isn't clear what "validate" is supposed to be doing. In the Tidy world, it seems to be checking that Tidy doesn't crash.
HTML5 spec has the notion of parse errors, but as expected, given that browsers encounter all kinds of html out in the wild, the html5 parser provides error recovery conditions for parse errors. Parse errors are only relevant for conformance checkers that might abort parsing on the first error, but is not a suitable response for browsers or wikitext parsers.
Looks like the capiunto extension uses this. As far as I can tell, the use in https://gerrit.wikimedia.org/r/plugins/gitiles/mediawiki/extensions/Capiunto/+/master/tests/phpunit/output/BasicRowTest.php#42 isn't really testing anything interesting. It seems like defensive code. BasicRowTest.lua just creates a table with a header and a row.
So, given that the lone use case is basically useless, I support legoktm's proposal to get rid of this mode from testing.