Trust me, the TV example was a really bad one to use.
I'll try another which you may or may not have heard of. 70 V line to voice coil. This is used to distribute sound at many speakers. Each speaker has a transformer with "taps" for the amount of power. L pads might further be used to reduce the volume.
Your "typical" amplifier is designed have an 8 ohm speaker connected. When you connect two in parallel, the resistance becomes 4 ohms. 8 in parallel, 2 ohms. So, this amplifier has to be designed differently. Higher currents mean higher losses.
In the real word, we might talk of a voltage amplifier or a power amplifier, but rarely a current amplifier. In electronics a unity gain amplifier generally has a voltage gain of 1, but has current gain.
Your AC power line, is constant voltage. When a power company adds more generating capacity, the amount of current that can be supplied will increase.
The TV example is a really bad one because there are cable length attenuations, the need for 75 ohm terminations, the need for no reflections, impedance matching, losses in the taps and splitters and even that current at high frequencies would actually prefer a hollow tube and not a wire. This is not elementary.