No, only if your grid is composed of "slow" power plants, you have to. That is why for a long time, all night-time energy usage was encouraged, to raise the base load. Ironically the outcome is used as an argument against renewables as it "but what about the base load"? :p

And if not completely dominated by slow power plants, there is always enough load on the grid to keep it stable. Especially in a day and age where there is a lot of storage, which can absorb some excess power production.

If I understood correctly, I don't think it's a good idea to waste energy to cover base load. It can be used for useful things instead.