Why are more powerful tools using higher voltage?

Matt already explained that using a higher voltage you'll have a lower current for the same power rating. This means thinner and less heavy wires, which means savings (copper is expensive). You may have to pay attention to better insulation, but that doesn't outweigh the advantage mentioned.

It's also much easier to place cells in series than parallel. When placed in parallel the voltages have to be exactly equal, otherwise you'll have high currents running from one cell to the other, causing big power losses and reducing the cell's life.

TLDR: Higher voltage is needed for higher rpm.

I disagree with copper efficiency argument (above/below)

The only reason is back EMF of motors at high rpm. No matter how much current the batteries can supply, their current translates to torque for motor, but not velocity. At top velocity, theoretical lossless motor has back emf exactly equal to the voltage of supply and consumes current approaching zero while having zero torque.

Higher power tools perhaps have higher rpm, rotational velocity figures, and they need higher voltage.

For exactly the same reason the power companies transmit power around the country at many hundreds of thousands of volts instead of just doing it all at 110/230v.

A higher voltage means a lower current for the same amount of power.

A lower current means smaller components and thinner wires, thus making it cheaper and more efficient.

For example, take a DC motor.

For a 12V motor to develop the same amount of power as a 24V motor it would have to draw twice as much current. This would mean that the windings in the motor would have to be made up of thicker wire. This would increase both size and cost.

The electricity companies transfer power at a high voltage so the current is low so they can use small diameter cables. It's all the same principle.