[throwway120385]

It's almost never a coincidence. Before digital switching everything was done mechanically, and before mechanical switching everything was done by people with plugs. If you have a big enough industry like telephone switching equipment then you're bound to see a lot of suppliers expand their market by selling the same parts outside of their home industry. Current flow is a nice signalling mechanism because you can tell the difference between short, open, and functional circuit. So I'm guessing it got used in telephone switching equipment and then preserved because there was no reason to change.

[cwillu]

And current through a wire stays the same on every point of the wire, more or less regardless of the length, as long as the supply can provide enough voltage to maintain it. This in turn dramatically simplifies the electronics needed to interact with it.