Like file downloads vs. interactive sessions, some power loads just need a long-term average and can be adjusted in time, without noticable impact, to shave peaks and get a closer match to generation - even if some of the generation, itself, is uncontrollably varying.
In fact, this is already being done. A prime example is in California, where a large part of the load is pumping of irrigation and drinking water. California utilities get away with far less "peaking generation" than they'd otherwise need by pumping the water mostly at off-peak hours. Cost: Bigger pumps, waterways (and in some cases "forebay" buffer reservoirs, below the main reservoir) than would be needed if the water were pumped continuously. This is practical because it was cheaper to upsize the water system than build and run the extra peaking plants. (Also: The forebay-to-reservoir pump generates when water is drawn down. It can also be run as a peaking generator, moving reserevoir water down to the forebay during peak load hours.) Similar things can be (and are being) done with industrial processes - such as aluminum smelters.
But there's a limit to load flexibility. Sure you can delay starting your refrigerator, freezer, and air conditioning for a few minutes (or start a little early, opportunistically), to twiddle the load. But you can't use such tweaks to adjust for an hours-long mismatch, such as the evening peak, or an incoming warm front leading to calm air and overcast skies on a chunk-of-the-continent basis. Try it, and your food spoils and your air conditioner (or heat-pump heating system) might as well be broken, or too small for your living area. Sure you can tweak factory load some. But do it too much and you reduce the production of billion-dollar factory complexes and workers who are still getting paid full rate.
Renewable energy actually helps - because its large-scale variations are driven by some of the same phenomena that affect heating and air conditioning loads. More wind means more heating and air conditioning load due to more heat transfer through building insulation. More sun means more air conditioning. Solar peaks in the day and wind in the evening (due to winds driven by the "lake effect" on a subcontinental scale), so a mix of them is a good match for the daily peak. But it's nowhere near "tweak to match generation and load without waste".