I stopped using Calibre because it turned out to be more annoying than simply emailing an epub to my designated kindle address. I've never had anything removed. Most of the content comes from libgen.
I can't remember all the specifics of how I set it up and honestly i've not used it in a while because I used it to get all my old Kindle purchased books on (which was a lot) and i've not booted the docker container since.
Is this a reasonable work around/alternative or have I misunderstood? If so, I apologise. Oh also, I think I had to do some custom stuff with my Kobo as well to support this functionality, but I don't remember it being difficult. Got it all wrapped in an evening of tinkering.
Minimal work if you configure the site as the homepage in the Kobo web browser.