I once saw some pretty smart guys doing things this way. I didn't discuss it with them so I don't know how much they tested and whether it endured.
The modern browsers mostly seem to support it. Many of the engines (Web Kit, Trident and Gecko) support the technique. It seems that KHTML doesn't which may not be important and it seems that Presto may get some things wrong (don't know what), so Opera might force simplified XSLT. With IE/Trident there might be a variety of XML engines MSXML2/3/4... for the same browser version.
supposition is that in 2001 it was hard to do but that today, ten years later, it may well be workable. (Provided that your XSLT is compatible back to earlier versions of MSXML if you want to support IE6. Though I wouldn't be surprised if most living copies of IE6 are beyond MSXML2.)
If there's a way of going beyond defining the transform inside the XML (kinda hard coded), it has some real possibilities. (I haven't checked whether that can now be done!)
You could render very differently from the same source without producing a different page for each version!
Testing is an issue. You want to test the actual DOM present in the browser, not the components from which it is constructed.
EDIT: To correct details of HTML rendering engines that support the technique, see Presto and KHTML.
EDIT 2, NOTE: KHTML is used in the Konqueror browser. I checked several years of log files (millions of server requests) for an internationally used site. Konqueror appeared twice. Once possibly as a browser (2 requests, which rules it out as a normal browser, maybe it was a robot) the other seemingly as part of a robot (2 requests). On that basis KHTML may not be important for many web sites.
EDIT 3, NOTE 2: Opera from Presto version 2.1 (at least) claims to support XML + XSLT. I tested an Opera 11 instance against a very simple XML + XSLT page. It worked.
EDIT 4, NOTE 3: I decided to dig a bit deeper. For run of web
content at least one user has developed a sophisticated handling system to avoid browser problems. Details at http://www.informit.com/articles/article.aspx?p=677911
. I imagine many publishers will find that intimidating. The article is 5 years old, so the current situation may be better
. For more detail on some issues Ivan Pepelnjak
has information at http://ajaxandxml.blogspot.com/search/label/XSLT
. Subject to better information coming in, I'll not pursue this at present.