It's not really excess electricity, but excess energy, and it's an artefact of how traditional power generation works: You generate electricity by creating rotation and using that rotation to drive a generator. Now, it's basic physics (conservation of energy) that if you add energy into a rotating system, it will spin faster and faster with every bit of energy you add, because the energy is transformed into kinetic energy of the rotation. The only way to prevent that speeding up of the rotation is to take energy out of the system--which, in the case of an electric generator you would usually do by connecting it to an electric load, i.e., the grid. But if demand is too low, you are removing energy from the rotation at a lower rate than it is added back from the mechanical drive side, so the net energy in the rotation increases and thus the speed of the rotation increases and thus the frequency of the electricity output increases.

Essentially, electric load is what brakes electric generators, if you take off the brakes but keep the motor running, they'll speed up.

My guess is that load acts as an inertial mass that adds drag to the turbines. Think of cycling downhill at the same power used when going uphill: you’ll spin like a crazy fool

I thought voltage needs to increase because a differential is required to add power to the network.