I've mapping the academic and news debates between schools of thought, Big debates, etc, make each one of those be a CPT.
But then to feed news articles into each, I found it easier to assign taxonomy terms to each that match each title, so that I can categories the news article to go straight to the CPT. This is more simple than create a relationship from news article to CPT. Plus, rss aggregators can only feed news articles to CPTs via categories, plus you can filter search results more easily with categories.
So, instead of creating matching taxonomies to parallel CPTs, (Schools of Thought, Author, Debate, Topic, Sub-Topic), can we just make these wordpress treat these CPTs like taxonomies?
Why not use the CPT-onomies plugin, I don't see anything that should conflict with Toolset.
Toolset builds on WP core. Post types are post types. Taxonomies are taxonomies. It adds features, such as post relationships, but post types mimicking taxonomies isn't one of them.
I'm not sure how that plugin works under the hood, but given that you mention it as an example of something you'd like to be able to do, I'm wondering, why not use it?
Unfortunately, it seems like the plugin maybe isn't maintained anymore, all of the links to the documentation from the plugin page are broken, they just redirect back to the plugin page.
The description says that they work with regular taxonomy functions and also taxonomy queries. This last part suggests it hooks into WP_Query—which is what Views are built on and are amenable to being modified—but without the documentation I can't really comment, I'm afraid.
