There are similar setups today.
I have voice over IP via fiber from Sonic. The house's old interior phone wiring is no longer connected to the telco in any way. So Sonic's VOIP box is plugged into the wall jack for the old phone wiring, from which it can reach some old phones around the house.
The main problem with this is that the Sonic-branded box is too dumb to manage power failures properly. The fiber modem/router comes up fine by itself, but, on every power outage, the Sonic VOIP box has to be unplugged and reset before voice phone service comes back up. Incoming calls are silently lost. The problem seems to be that the VOIP box comes back up before the Internet link is fully operational, confusing the VOIP box.
Have you considered using a power on delay relay? There are many for refrigerators that feature a ~5 minute delay and are quite affordable ($6[0])
We have started a house "lab notebook" documenting stuff as we find it so that we aren't starting absolutely every project from zero knowledge.
We replaced the bedroom ceiling fan this summer, and discovered some "interesting" things about the rest of the wiring on the second floor. I added some notes for future me so that when I go to replace the sconces later this year, I don't have to figure out the weird wiring for them a second time.
I highly recommend doing this for your own sanity and for that of any future owners.
Back in the dial-up days once call waiting was introduced you were routinely instructed to disable it. I had a box sort of like the fax switcher that I purchased on ebay that would instead listen for the call waiting tone and the box itself would ring, allowing me to pick up the phone attached to the box and receive the calls. It solved the problem of being able to use the phone line for hours on end for internet downloads without losing the ability to actually receive calls.
I also found if I identified a spam call fast enough I could hang up and switch back to the dial-up connection before it was dropped. I had to be real quick but I could usually avoid being dropped from a Starcraft match.
She describes exactly why networks are star configured and feature IDFs and MDFs. Even in analog phone days, commercial installations had telco closets where circuits were distributed. Residential not so much. My condo built in 2004 has the lovely feature of daisy chained network jacks. The only way to make the last jack in the chain work is to patch through all of the other ones. Fortunately wireless is a thing
All the phone jacks in my house come after the kitchen; and there's a short somewhere. So we can only use the kitchen jack unless we figure out where the problem is. And that is, unfortunately, about _this_ much more work than I'm willing to put into it.
Shouldn't feel bad about it, really. It's your/their house, and anyone buying a house (even brand new) should be expected to find all sorts of random and weird junk.
And now telephone lines themselves are rarely if ever even used anymore; the last ones I've seen have just dumped into a DSL modem.
A competent telephone technician with a toner would easily figure out what's going on.
I'm not sure, it took three techs three tries to figure out that the previous owner had hard-installed a DSL filter in the demarcation, and then painted it to look like part of the box.
In case you think fax is now ancient history, there are tens of millions of faxes still crossing the PSTN every day. Fax is alive and well!
They don't work the same way they used to though. Since old school PSTN hardware is being replaced with VoIP, there is a hacky protocol called T.38 which does just enough to convince each side that it's talking to a real fax, and decodes and forwards the data over IP.
T.38 is actually a fine way of transporting fax bits but unfortunately it is quite uncommon to see T.38 end-to-end. While a VoIP provider may negotiate T.38 with a customer's fax ATA, it is likely being transcoded to G.711 by a gateway at some point as it traverses the telephone network, ultimately making T.38 a less-reliable choice. (Better to have the same codec end-to-end.) A comparison might be cellular or VoIP providers offering wideband codecs, which sound great when you stay on-network, but when the call crosses the PSTN and is transcoded, the sound is worse than if you used the standard narrowband end-to-end.
Circuit switched class five offices are still very plentiful though, and DS3-based transit networks are still nationwide. So if you want it, you can absolutely still experience phone networks without voip.
In Japan they are still widely used by businesses of all types. In the US, I see them routinely in doctor's offices for transmitting signed orders etc.
In many, MANY workflows a fax is considered "as good as it gets" for a signed copy of a document.
The same thing scanned and sent over email? Many not so much.
This is why analog was better, easy hacks.