For example, if my website's listings properly display the breadcrumbs rich snippet, but do not show the aggregate star rating rich snippet, should I assume it is something in the structure or is Google intentionally suppressing these?
All you have to worry about is what Google tells you. Just use their structured data tools and fix everything what is needed to fix. https://developers.google.com/search/docs/advanced/structured-data
If everything looks fine there, have patience. Meanwhile fix the errors you find within your search console. 😊