Baseload is quite irrelevant, because baseload also doesn't supply those critical needs. "Baseload" is by definition power production that can't follow the demand curve, and thus can't provide the power to keep the grid stable. It's as bad as solar and wind in this way, it's just that instead of having a fixed but variable supply curve it has a fixed but flat supply curve.

What you want is dispatchable power. Gas peaker plants for instance. Or overbuilt solar + batteries. Not baseload.