The advantage of XHTML syntax is that it is XML. It can be easily parsed, understood and manipulated. The HTML syntax is a lot harder for clients to work with.
Nonsense! The HTML5 spec defines how to parse HTML in a way that is relatively easy to implement, and off-the-shelf parsers are being developed that can be easily integrated into tool chains. It’s even possible for an HTML5 parser to be integrated into an XML tool chain in place of an XML parser.
But what you need to understand is that in practice, you’re most likely using HTML anyway, even if you think you’re using XHTML based on the DOCTYPE. If your content is being served as text/html, instead of application/xhtml+xml or another XML MIME type, then your content will be processed as HTML.
With HTML5, you can choose to use HTML-only syntax, meaning that it is only compatible with being served and processed as text/html it is not well-formed XML. Or use XHTML-only syntax, meaning that is is well-formed XML, but uses XML features that are not compatible with HTML. Or, you can write a Polyglot document, which is conforming and compatible with both HTML and XHTML processing (In principle, this is conceptually similar to writing XHTML 1.0 that conforms with Appendix C guidelines).