It's important not to forget that Document people had been dealing
with this stuff for over a decade before XML.

My thinking about presenting it to procedural programs is to emphasize
that essentially the data makes "function calls" to the templates
(which is the opposite of how procedural code works, where the program
is in charge of flow, in XSLT the data is in charge of flow... my
thinking on this is still pretty immature)

Only for the default case, where elements are presented for
processing in document order (and I don't see how else it could
be written...). Anything else it's XSLT (or rather, the programmer)
which is in charge.