> browsers simply didn’t use XHTML
Do you mean "developers didn't use XHTML"?
All browsers implement XHTML. It's referred to as "the second concrete syntax for HTML" in the WHATWG spec.[1]
Indeed many websites do use XHTML, the HTML application of XML. However, since proper documents render identically, you won't be aware that you're visiting an XHTML site - that is, unless you check the source.
Fun history side note: Browsers like Netscape and Internet Explorer didn't agree on how to parse HTML in the past. They handled omitability differently, for example, in overlapping hierarchies (<p><b></p></b>). To fix this mess, Sir Tim asked well-respected SGML practicioners to create a clean subset of SGML and define a document type definition (DTD) for HTML. They came up with XML, the clean subset, and XHTML, the DTD. [2]
Basically, XHTML was the first actual standardization of HTML. Unfortunately, minor syntax errors will prevent a XHTML document from rendering, which, to some degree, is probably why it was never widely accepted by developers.
[1] https://html.spec.whatwg.org/multipage/introduction.html#htm...
[2] https://www.youtube.com/watch?v=Q4dYwEyjZcY