Now that is insane. Totally sounds like one of those things that paranoid old people believe about newfangled technology, but nope, just extremely weird protocol design.
Its not really weird if you look at it in context.
People who are not Gen-Z whipper-snappers will recall the era.
Before cell phones, before DECT home phones, before wireless cordless home phones you had fixed phones.
You had a master socket and then, optionally, one or more secondary sockets (depending where you lived, you were either permitted to install these secondary sockets yourself, or you had to call in the telco to do it).
Anyway, so what would happen is that your friend from school would call you up. Inevitably your parent would answer the phone because they were, for example, in the kitchen cooking your dinner.
There would then be a shout across the house "Bobby its Johnny ... AGAIN !".
The call-transfer process would involve your parent hanging up and you picking up the nearest secondary handset.
Hence the exchange needed to keep the A-end of the call live whilst you completed the B-end "transfer".
The same generation of people will also recall the ability to abuse the mechanism to quietly spy on someone else using the phone. :)
"Called Subscriber Held", a feature that was carried into early digital exchanges because people expected it to work in the manner you describe, even though afaik it was designed for the other purpose of keeping the line open whilst operators patched it through, trunk lines picked up the tone, etc.
My grandpa was a something like chief engineer for the West Coast of Scotland phone network. I have so many questions I wish I could ask him these days.
Remember it used to be a switched physical circuit. In the early days the switching was done by people, later it was automated. But you still had a circuit from phone to phone.
When one side hung up, the circuit is still live. Eventually it timed out and the switch disconnected it, but it took a while (don't remember how long). So you could hang up a phone, walk to a different room and pick up another phone and the same call circuit was still live (as long as the other side didn't also hang up meanwhile).