Looks like an interesting read, I'll finish it in a minute, but I just want to say, as someone working in a medium profile public institution...
Yeah our PR team would love this idea. What would actually happen is that nobody would read our updates, except that one or two journalists who repost it immediately on Twitter and X.
A "medium profile public institution" can not make their own gravity, like La Liga can.
For them, I'd recommend to take a POSSE [0] approach: create their own instance and treat the other platforms as mere syndication channels. This would allow them to not lose any of their reach, but would also signal to everyone else that an exit path is available.
[0]: https://indieweb.org/POSSE