Besides some papercuts / browser bugs like "refreshing the page desyncs the inspector", the main issue I find with it is I don't see how I can modify things dynamically?
By the time JS runs, it's on the resulting HTML DOM, not the XML source, so I can't add elements dynamically respecting the XSLT stylesheet?
Also, XML must be well-formed and have a single root, I can't stream it out on the server piecewise?
With those 2 limitations, I don't see any advantages over any other server-side templating language, it just duplicates work that could happen once in a SSG or at least cached in a CDN, onto every client computer.