What am I missing?
When you step into a full bathtub, the water level rises instantly everywhere. Yet your foot-meat didn't leave your bones and fly outwards to all points! The water only moves slowly. How could the water level rise instantly? You're missing the concept that wires are not like hollow pipes. Instead they're already full of mobile charges; typically ten thousand coulombs per cc.
Wires act like bathtubs, or like long canals, where if you stick your foot in (or pour more water in,) the water-level rises everywhere, seemingly instantly. (Go fill your tub and try this!) Yet the water itself barely moves, and some blue-dyed water which you added stays where you placed it.
You'll discover that with very long canals, the distant water-level doesn't rise instantly. Measure the delay, and you find that it's caused by the speed of sound in water. So, when you step into a bathtub, your foot must be sending out a high-velocity pressure-wave which pushes the water outwards, and forces the water-level upwards. The water is the medium, and only moves slow, while the wave propagates at enormous speed. It works similarly for wires. The charge is the medium and the energy is the wave. Coulombs and amperes describe the medium, while joules and watts are measurements of the waves.
The second thing you're missing: even with zero-ohm superconductors, if you wind a coil, the inductance won't be zero. This means that any sudden changes in potential cannot spread instantly to the whole wire. True, for zero-ohm conductors there cannot be DC potential differences anywhere. But AC is a very different matter, because impedance (reactance) then plays a role.
Make a shorted one-turn inductor using zero-ohm wire. Now stretch it out, make it into a narrow loop 300,000KM long. It won't be a simple inductor anymore, because the two sides of the circle are spaced closely, and have significant capacitance. Next, cut one end of the loop and suddenly insert a battery. The shorted loop will obviously draw a current, but it won't be infinite, even with zero-ohm wire. Instead the loop will act like a resistor of a few hundred ohms. Sound familiar? There's a wattage going outwards from the battery, and joules of battery-energy seem to be vanishing into the zero-ohm wire. The energy is being stored as a magnetic field surrounding the two halves of the long loop, and also as an e-field between the two halves. A long, long "sausage" of EM field-energy is spreading out along your narrow loop, and since the loop provides a load on your battery, the loop must act as a resistor. Weird: make your loop much shorter or much longer, and this "resistance" remains the same!
If there is a light bulb connected into the far end of your 300,000KM loop, the battery will light it up, but after a delay of one second. The EM fields spreading along the loop were moving at the speed of light in air. Try adding heavy plastic insulation to your loop. Yep, it now takes longer for the light bulb to flash. Your loop is a waveguide for EM. But not for microwaves, it's working at DC! The name for all this stuff is "transmission line." A transmission line is an EM waveguide, but unlike hollow microwave waveguides and optical fibers, it operates independent of frequency. It works fine all the way down to 0Hz.
The math behind all of this was worked out by Oliver Heaviside, who was trying to figure out why Morse-code dots on long telegraph lines were getting stretched out and blurred as they traveled. He discovered that, if we add the wire-resistance back in, then waves of different frequencies travel at different speeds, all a bit slower than "c". Lol, conspiracy theory, he was attacked in print and nearly silenced by W. Preece who ran the British telegraph system. Then he had his ridiculed ideas stolen by M. Pupin of Columbia U., who became a multi-millionaire by patenting them and selling them to Bell Telephone. This cured the unexplained distortion which made voices unintelligible on phone lines longer than miles. So, essentially Heaviside invented the long-distance telephone network. Look up Heaviside's "Telegrapher's Equation." And as with all of these stories, after his enemies got rich off stolen ideas, Heaviside died penniless, and didn't become world-famous until later.