Two things - (1) as you can see below, some syntax search resources lack templates and (2) will there be templates for the Morph Query?
I know the question about templates and syntax queries has been asked and answered elsewhere, but the two above that have no templates are really the same syntax database schema with two different texts. These are the Lexham Syntactic Greek New Testament (LSGNT), the NA27 and SBLGNT versions (I don't know why the name of one changed).
There really aren't any appropriate templates for the LSGNT. Most of the interesting stuff is the syntactic force data, at the word level. And there are scads and scads of them; it would mean making over 100 templates, and those for things that are more easily found (and seen in search results) using the Lexham Syntactic Force Supplemental Dataset.
So I'd say just because templates are a supported feature of syntax databases it does not necessarily follow that all syntax databases will have templates.
On Morph Query, I have no idea.
Thanks Rick ... that makes sense ...