This. When I contacted Amazon about missing contents from Crunchyroll Channel they told me some contents are exclusive to Crunchyroll'S own website due to streaming license, and I told them then they shouldn't advertise and claim that the customers get "full access to the Crunchyroll library" (okay technically it does, since Crunchyroll allows you to link your Amazon account to your Crunchyroll account, but that's beside the point).
I'm not sure if this was by design, or it was simply overlooked, since some of the missing contents were added to Prime later. But on a business point of view, it's not optimum for Amazon to wrestle extra contents from channel providers. Prime channels are a bonus for Prime members, you can't use it without a Prime membership. Most people subscribe to Prime for the free 2-day shipping, but even without a Prime membership the minimal amount for free shipping is easy to achieve. Freevee also has plenty of good contents customers can access without a membership. Extra/exclusive contents alone are not enough to entice people to shell out an extra $140 a year, unless those channels are free. If it's streamer-created contents there's nothing to gain for the streamers, if it's 3rd party contents Amazon can easily obtain the streaming license for itself.