Green Energy

or that the idea of turning them off is simply inconceivable (why would I turn mine off and let others make money)

If that's the issue, it seems like time-of-use rates or smart metering could be an easy solution. If the price of electricity were negative during periods of oversupply, I bet people would figure out how to disconnect their solar panels pretty quickly. This pricing model would simultaneously incentivize energy storage projects.

With spinning turbines, the issue is, that you need to maintain a constant speed of the turbine at all times. That rotation speed directly correlates with the mains frequency of the attached generator. That's either 50 or 60 Hz depending on where you live. If the load increases the frequency drops and the turbine speed decreases, when the load decreases, the opposite happens. The people maintaining the grid have to make sure load and supply are in balance to keep the frequency stable and the trubines within their operating parameters.

Compared to that, solar panels have none of these constraints. For one, they output DC voltage not AC, and secondly they don't mind at all when there is no or very little load. The DC voltage is electronically converted to AC by an inverter. Such an inverter synchronizes its frequency with the frequency of the power grid. So you can easily simply disconnect solar panels when there is too little demand without any issue. You can't easily do the same with a power plant with a turbine. If you were to remove the load from a turbine, you could actually destroy it, if you are not very careful.