xsl:iterate works but it's limited to a single level of iteration, as
this way one cannot easily collect output from nested transformations.

Yes, that's correct. The use case for a single recursive tree walk of the input that delivers multiple results was one that the WG found particularly taxing; we tried many different design approaches. The solution currently in the spec (but not yet implemented) is xsl:fork, which essentially allows you to do several traversals of the input tree "in parallel", each delivering a separate result.

From the output perspective isn't it opaque whether xsl:fork is used?