Hi Joan,
I hope it is appropriate for me to chime in, since my day job as a funded project monkey prevented me from attending all but one ParGram meeting in the past.
I'm now trying to get back to doing more linguistics, but with the perspective of the needs of the field of language technologies.
Here is how I see the importance of ParGram:
1. Cross-lingual studies of grammatical relations, information structure, constructions in a very broad sense, argument realization, grammaticalization, etc. leading to theoretical insight into the nature of these things.
2. Treebanks and parsers that can be used for corpus-based studies in linguistics, and perhaps in some hybrid third-wave neuro-symbolic systems in language technologies, especially in low-resource languages.
3. A challenge to UD (universal dependency) and UMR (uniform meaning representation): I think we can learn from UD and UMR how to do things on a larger scale. But at the same time, we can save them from their fate as stone soup in the following sense: they thought they could do something easy (make soup using only "stones" and water, which consisted of three pages of definitions of grammatical relations), but as they progressed, they needed to keep adding "carrots", "onions", "bones" (serious linguistic decisions). But unlike the story, where the soup turned out good, UD has turned out messy and too big to fail. Sometimes they talk about possibly not going on to Version 3 because Version 2 is too big to change. We can show how to do a UD-like project on a firm foundation.
--Lori