I think asking for private live streams to be hosted on this hypothetical platform might be a bit too much in terms of hardware cost/ technical needs, (especially in my imaginary idea of the platform being open source and plug and play) but maybe an alternative would be: ability to send subscribers a link to a private stream, or embed a stream from an alternative source and have a chat for subs, utilizing alternative streaming services such as stream.ninja / odysee/ owncast / stream.place / zap.stream / there are more, the key is finding one that fits your needs (ability to do private stream), you can find a ton of platforms by checking what platforms socialstream.ninja supports
but the function of the platform in this case would be the ability to have fans support via monero and gain access to these private streams(+ other private content such as newsletters, art content, ability to be sent physical items like rewards, yknow the usual patreon stuff), which has an underlying technical layer regarding maybe email newsletter (or better yet, integration with private messaging apps in lieu of email for notifications) functionality, ability to identify subs to give them access to things, etx.
sorry for the word wall, I have too many thoughts in my head! this could be a very valuable project for not just monero but the entire alt ecosystem