Canonical URL breaks caching?

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I was/am having performance issues with a couple of C5 sites. After days of messing around with this, I've found that when I set a canonical url in order to secure the site, caching no longer works.

In SEO & Statistics -> Urls and Redirection:
- set Canonical URL to "https://www.example.com"
- set Canonical Tag to checked, or true
result: pages are no longer served from the cache

In SEO & Statistics -> Urls and Redirection:
- set Canonical URL to ""
- set Canonical Tag to unchecked, or false
result: pages are served from the cache, but with http protocol for URLs. Pages served over https produce a warning in the browser. Forms can only be POSTed if they are requested via http protocol.

In SEO & Statistics -> Urls and Redirection:
- set Canonical URL to "https://www.example.com"
- set Canonical Tag to unchecked, or false
result: pages are served from the cache, but with http protocol for URLs; this means forms cannot submit and pages served over https produce a warning in the browser

Am I missing something here, or is this the expected behavior?