The solution to the baseload problem is flexible demand. If it is cloudy and non windy, don't smelter aluminum, to put it bluntly. It is pretty easy, but we have to adjust our expectation of having 100% power at all times, and of the private sector being able to exploit it to 100%.
Solar, wind, water, geothermal, biogas and battery storage together are more then enough to "keep the lights on" at all times. And in peaks we can already produce more renewable energy than we can use. It is "just" a matter of investing into storage and flexible consumption.