I'm sure there are countless incredibly legitimate use-cases for a technology like this, but there's part of my brain that seriously wants to explode at the notion of coupling Node and XSLT.
For example, XSLT lets you decouple the content structure of your document from the presentation structure. XSLT makes nested <div> obsolete. It lets you have responsive HTML—you can serve different stylesheets to differently sized browsers (or switch them on-the-fly with JS). In general, what it can do is cool, but using it is not. If XSLT weren't something of a trainwreck the web would be in a better place.
How come Web has stuck with HTML and CSS is beyond my comprehension. It's like selling their firstborn right for a bowl of animations.
As an alternative to XSLT consider CDuce language. It was made to solve a similar problem: XML manipulation. But language itself uses traditional syntax and much easier to use and understand.
XSL is a little bit like CSS in one way: CSS has selectors, and XSL does too. CSS also has rules (one or more selectors and the properties listed for them) that apply to an output device's representation of the nodes matching those selectors (e.g. a browser's visual styling), and XSL has templates that change the structure of the nodes that match the XSL template's selector. Each template has a context, can transform the input "tree" to any intermediate representation necessary, can apply itself recursively, and can completely transform the XML-structured input into practically any output required.
It's also a religion along the same lines as vim/emacs/atom or Mac/PC/Linux/UNIX/BSD/etc., and thus, discussions decrying the blasphemy of declarative transformations will result in fervent cries of, "XSL sucks, nuke it from orbit," as well as equally impassioned speeches that, "XSL kicks ass, get enlightened!"
E.g. I remember having a large project I initially split into multiple XSLT files; in the end I wrote a XSLT to take them all and combine into a single file.
There's also a cadre of people, colloquially known as 'XML guys', that do use XML the right way.