In the few factories I have worked the power hungry processes cannot be stopped on demand (eg. one day notice), as it would waste products, it would mess up minimum stockpile lean manufacturing, as the process cannot be interrupted, it could often damage equipment, and usually restarting these processes is very expensive in terms of energy (eg. Reheating a kiln)
The renewables are simply not predictable enough for this, that is why nuclear, an later fusion power will have its place in the energy mix in the foreseeable future.
Long term, this becomes a matter of calculation. For some businesses its is possible and cheaper to adapt their energy consumption to the spot market prices of electricity, for others it is not, they can decide either to have some storage facilities of their own, or pay the utilities companies to provide the full load 24/7.
You're right; many of these facilities go so far as to install backup Diesel generation on-site.
There are plenty of opportunities for demand-shaving, though. The simplest one is to simply reduce the HVAC load by adjusting the thermostat.
I agree we need some nuclear, too, at least in the short term; it's not an either-or proposition. We need nuclear AND renewables AND smart grid AND storage.
The paper mill near here has one of the larger power plants (biomass, burns waste wood) in the region. It uses more power than the nearby small towns combined.
The best way to get industrial consumers to switch is to drive down costs. We're certainly nowhere near 250 Megawatt-hour batteries being cheap and commonplace, but there are projects of that scale that have been announced (in particular I'm thinking of the Vanadium flow battery being installed in China).
The renewables are simply not predictable enough for this, that is why nuclear, an later fusion power will have its place in the energy mix in the foreseeable future.