Even XPath 3 is Turing complete
You would never want to write a JPEG decoder in XSLT, but the fact that it might be possible if you were willing to bend over backwards, write unmaintainable code that runs incredibly slowly and requires colossal amounts of memory, misses the point.
I thought the point of XSLT wasn't really arbitrary processing but to transform XML into other formats (mostly, but not always, other forms of XML such as XSL-FO) - and it was reasonably good at that.
DSSSL was extensible in Scheme, so all transforms had access to arbitrary processing, by the standard.
Lots of people got lots of work done with Microsoft's non-standard scriptable XSLT, because they believed it was just too hard to get anything of interest done in standard non-scriptable XSLT, but worth paying the price of being locked into Microsoft's ecosystem.
(in reply to arethuza's reply:)
Here is an raytracer written in XQuery: https://dev.w3.org/cvsweb/2011/QT3-test-suite/app/Demos/rayt... (imported modules are in the directory above) looks quite maintainable to me.
XQuery is pretty much XPath-with-functions, and XPath 3 has anonymous functions, so you can directly translate it to XPath 3 by replacing `declare function foo(..` with `let $foo := function(...`
Once it is XPath, you can put everything in a xsl:value-of tag.