You do not need a wire to transfer electrical energy. You do need a wire to harness electrical energy and turn it into something else (e.g. light).
Derek posted a video on his Veritasium channel about the big misconception about electricity. You don't have to watch it, as I will summarize it below, but I highly recommend you to.
A thought experiment
If we have a circuit that's 3*10^8 m long, and only 1m wide, how long does it take to turn on the light that's 1m away from the battery?
What powers a light bulb
It's the movement of electrons that actually lights up the light bulb in your house. Either it's an LED powered by direct current, where electrons move in one direction or it's an incandescent light bulb powered by alternating current, where electrons oscillate, it's the movement of electrons that delivers the energy to the bulb. But that only describes how electrical energy gets delivered to the bulb – not how electrical energy gets moved from a power plant to your house.
How to transfer electrical energy
This is what Derek's video is about. A common misconception is that the electrical energy is transferred through a wire. It's technically not wrong. It's just that electrical energy is not only transferred through a wire. It boils down to can we move electrons remotely without being physically connected? Of course we can. Capacitor is a living example. The battery, or power source, can move electrons remotely via electromagnetic field.
Light bulb in your house
So how does the light bulb in your house get its electrical energy from – or who's moving the electrons?
- A power plant first turns wind/solar/etc. energy into electrical energy.
- AC eventually reaches the transformer that is closest to your house, which transforms the voltage to 110v (or else depending on where you live).
- Now you have 110v alternating current, oscillating the electrons that are already physically there in the wires. So since you own the wires, you technically own all the electrons in them. When you pay electricity bills, you are not buying electrons because you already own them. You are buying the energy that oscillates them.
- The energy that oscillates the electrons (within the wire) comes from the electromagnetic field around the wire. You do not need a wire to transfer energy, which shouldn't be surprising given all the wireless chargers around. You do need a wire, to harness the moving electrons, to turn the electrical energy to something else. That's why if you cut the wire to your light bulb, it will not work, which hopefully shouldn't be a surprise.