Standard telephone wire is 24 gauge. It does carry quite a voltage on it. If you've ever been splicing wires and had the phone ring you'd remember. It gives quite a tingling sensation in your fingers. I had one poke me in the eyeball when the phone was ringing once when I was rewiring the house. Not fun. The wires already get pretty warm when you're on the phone for a while. As far as I know, telephone rings are in the 50 volt range. That's half the voltage of 12 or 14 gauge electrical wire on wires 1/10th the diameter. I don't know exactly how data rates translate into voltage, but I imagine junction boxes would heat up pretty good if we used faster rates.
Telephone wires can't really get much bigger than what we have now for the simple reason that if they did, they'd be near impossible to splice. Junction boxes have hardware in them specifically designed for 24 gauge wire. Thicker wire would mean upgrading every junction box in existence. In a lot of cases the telco doesn't even know where these are. The one for my house is in a forest in the back (it wasn't a forest when the box was placed; it grew around the box). I have to tell the Bell techs were to find it every time they come around here.
The wires are thin specifically to make them easy to splice and connect to existing hardware. I don't think it really has anything to do with older technology.
And Alexander Bell was Canadian. That would make Canadians the pioneers of phone tech, although he did most of his work in the US.