What I hear you saying is, they'd need to build out an actual CDN service that individual companies would have to sign up and use. This service would allow Starlink to be able to use their own certs themselves or have the owner's certificate.
My understanding is Cloudflare's service works this way. I believe this would be a good partnership between both companies.
I'm guessing the other approach is similar to Netflix's open connect. Where Netflix is given the option to run what they normally run on their open connect boxes but in a virtualized environment on the satellites themselves.
Now, I know that wouldn't seem all that practical if the service was seen as something anyone could sign up and buy because it isn't like these satellites are the same as EC2 instances and it isn't easy to just rack a new one but my gut feeling is that a very tiny portion of content is a substantial amount of bandwidth.
Edit: Even further, if they're launching 12000 of these couldn't that be a CDN network itself?