You don't need closing tags for a specification to be strict. As long as you define the parsing rules rigorously as HTML5 does, there is little benefit in XML compliance and there is in a well defined non-XML standard as it is mostly backwards compatible.

One of the possible definitions is a mode of HTML that was forced to be strictly validating by an XML parser. Adoption of this was hurt by the fact that XHTML-delivered-as-XHTML didn't work correctly in the dominant browser of the time. But HTML5 also delivered a fully-specified parser that explained how to handle tag soup correctly, which meant the problem trying to be solved here (having to parse HTML files into a DOM) was solved in a different way.

Another possible definition is the XHTML 2.0 definition, which tried to rip out a lot of HTML features and replace them with more semantic definitions and was largely an effort that was entirely divorced from reality (to the point of driving out the web browser implementors entirely from the working group).