Firstly, power stations don't send power both ways. They don't even send power. They send energy, and they only send it one way. Power is how fast the energy is being sent.
An analogy: you can send babies. You can't send birthrate.
What is going both ways in the circuit is electric charge. And, since electrical power distribution is usually AC, it's only going both ways at an instant. If you watch it over time, you will see that it reverses direction about 50 or 60 times per second, depending on national standards.
An analogy: the wires are a long rope, your toaster is a pulley, and the power plant is someone holding the ends of the rope, with the middle looped around the pulley. The power plant pulls each end alternately, and the toaster heats the bread with the friction generated.
Now consider what you mean by "grounded". The schematic you have drawn is really shorthand for this:
simulate this circuit – Schematic created using CircuitLab
If by the ground symbol, you mean, "connected to a copper rod in the Earth", then we have to consider what's between the copper rods. It's not a wire.
Rather, it's some soil, which conducts, but not especially well. You could roughly approximate it as a resistor. Consider, what would happen if you inserted a resistor at the bottom of this circuit? If it's not very small relative to the resistance that's already there (R1), then a significant fraction of the power (the rate of energy use, not the stuff in the wires, remember) will be lost in the Earth. This makes the distribution very inefficient.
However, there is a type of electrical power distribution that uses only one wire, and uses Earth as the return. It's called single-wire earth return, and it works (to a gross simplification) by delivering the energy at a higher voltage, thus reducing the current in the Earth, thus reducing the losses there. At the delivery point (your house), the voltage is stepped down to 120V or 240V or whatever your national standard is.