Life is like riding a bicycle: if you want to stay in balance you have to move.Albert Einstein
Beyond the legs there is more: why train the core
You can have all the strength in the world in the legs, but without a stable core you won't be able to use it efficiently.
This is the area where the movements originate, the one that more than any other is responsible for stabilizing the trunk and ensuring that the force exerted is transmitted without any loss of power.
In fact, Graeme adds:
A solid core will help eliminate unnecessary upper body movement, so all the energy you produce will be channelled into the pedal stroke.