These approaches always measure the wrong thing though - the average carbon cost of electricity.

What you need to know is the marginal carbon cost, which will be much less variable as almost all dispatchable generation is fossil.

So yes, you should avoiding adding load when there is a severe supply crunch and the marginal power is generated by gas peaker plants (often gas turbine based), and use power when renewable generation is otherwise being curtailed, but most of the time the grid is firmly in the middle regime with a fairly average marginal cost.