Chances are, you're already running one.

If you have a smartphone, it allows the carrier (=client) to access the device (=server) remotely.

Same for cable modems.

Maybe you also have a Wifi router. It is listening for HTTP requests because it has a "Web GUI". It is thus a web server, among other things. Maybe it also has a "backdoor" for remote login as reports continue to show this is common.

The idea is your devices are listening for incoming connections and they have data stores to serve on demand.

You may disagree but I would call these servers.

Many people manage to setup Wifi routers at home.

And with a modem or smartphone, there is almost no setup. You just turn it on and it starts serving.

So, I'd argue that "running your own server" is actually something anyone can do.

Maybe the real barrier to "running your own server" is only just confusion over terminology.

How would you ensure operational continuity for my mom who only has an ipad? Since that's the direction the world seems to be taking.

You can cache the data. I mean just think about how Git works. You can sync the information at random intervals between peers, and you don't need a direct connection all the time. A well-designed P2P decentralized network solves all these problems. A can send to C through B, if A and C are not currently connected and so on.

In fact, these are solved problems, and implemented in e.g. Freenet as far as I know.

Server/router hybrids.