The more pressing problem is industry, which makes up about 44% of our electricity. Some processes, e.g. metal and glass smelters, absolutely require years of uninterrupted power supply or need dozens of millions of euros and months of downtime to get repaired. Some, like electric-arc aluminium smelters, can handle a short-term load disconnect and receive a premium on their electricity prices for that. The utter majority however could in theory be suspended and resumed at will, adjusting to market prices and stability requirements... but the owners don't like that uncertainty and workers don't like it either because they wouldn't get paid.
Other large consumers like city lighting or advertising could in theory also be shut down or reduced during peak demand times. But as we've seen in the winter following the Russian invasion of Ukraine where that was outright banned by an emergency decree, this is politically untenable - people have grown so accustomed to the luxurious energy waste that they're (literally) willing to kill over it.