> ...Tell me why, even as a nerd, I want to run a server...
Actually, you have the *choice* to run a server or not. (Conceptually similar to old school email, you can live on your own server, or live on someone else's servers.) For matrix (or heck even for email) if you do not wish to manage your own server, there are free and paid services that you can leverage.
> ...instead of them opening the built in app and just having at...
This is not clear to me if you were referring to Apple to open up their app or if you meant matrix. Because i agree that Apple should open up their app....Even though i am a matrix fan. More open apps helps everyone involved to communications plaforms (including and especially users). But, if you meant for matrix to have their app open...well, matrix is the open protocol, and there are already many opened apps, such as Element, Cinny, Fluffychat, Schilid, etc.
> ...and get my friends and family to join to chat...
Yeah, no matter if Apple opens up or not, the network effect of asking/hoping friends/family join something else is real and non-trivial. Matrix won't solve that alone, because its not necessarily a tech-only problem. My personal hope is that - whether it is matrix protocol and associated clients, servers or something else entirely - i do wish we had some universal, open protocol that allowed for everyone, everywhere to chat...and which was not controlled by a few, powerful entities.