Or actually radical: switch from our terrible first-past-the-post voting system to - say - ranked choice (or one of many alternatives; they're almost all better than fptp) and then primaries won't be so important and parties won't have so much power over our kinda-democratic-but-actually-oligarchic political system.
The answer depends on the specific CRDT algorithm in use. For complex data structures like the ones behind collaborative text editing your intuition that the updates end up looking hierarchical is generally correct.