Yeah, but how do you make a copper wire heat up without also heating up the wiring that leads to that copper wire? You can make it thinner, but these bricks aren't very thin.
Induce a current magnetically and you don’t need a direct wire connection. As for what to put in the intervening space I will leave that as an exercise.
Induction cooktops are ridiculously efficient at heating
You've probably seen multiple instances of this in your daily experience. A fuse is a thin conductor between thick electrodes. A light bulb is a very fine conductor between thick electrodes, encapsulated in a vacuum bulb. If you use tungsten electrodes, you can easily melt copper in the manner I've described -- that's how TIG welders work.
Responding to your question about electric current:
Quite simply, use leverage! Take a transformer with multiple (N) windings on the primary and a single winding on the secondary. Putting one (DC) amp through the primary will induce N amps through the secondary. With induction, you can use a low current to induce high current. Or correspondingly, transform low (AC) voltage to high voltage -- this is how high voltage power lines work.
True, but something should be there to close the loop on that not-so-thin brick, and that something will get hot. That picture shows only a single brick, not a loop of bricks so something does not add up.
You stick a large high temperature electrode into molten copper. This is how an arc furnace works. Some have water cooled electrodes to keep them from melting.
Induction cooktops are ridiculously efficient at heating