If you examine the cable going into your modem or TV set you'll find that, besides the shielding telephone lines lack, it too is "shoved into a copper wire". One wire of copper or aluminium depending on where you live. This is a direct outgrowth of old-fashioned TV antenna reception. Broadcasters kept stringing wires to more and more broadcast towers, while consumers kept stinging longer and longer lines to bigger, better rooftop antennas, which served entire buildings or small neighbourhoods. At some point, we found it expedient to simply splice these overlapping webs of antenna systems together, and quit using air as an intermediary. This sprawling web was still essentially an antenna and still received air transmission.
The shielding came in when cable companies realised it would not only clarify reception of their own channels (or allow greater bandwidth, depending on how you look at it), but allow them to restrict the available channels. With blockers on the pole outside every house, they could selectively limit consumer reception, based on payment. Later, the cable companies tried a number of ploys to restrict channel availability within buildings, even to each individual set.
So, cable clearly has the jump on bandwidth over phone lines, since they've been pushing that envelope for decades and have pretty well reached the limit, but phone lines in many areas already exceed cable's bandwidth, and we can safely expect doublings in telephone bandwidth as lines are upgraded and voice devices grow less demanding.
I have a grudge against cable companies too, since their mode of "service" is in fact to restrict something available to all, their operating costs going mostly to enforcing that restriction. As for unrestricted computer access though cable, I see no light at the end of that tunnel.