> But many appliances like the fridge have low average consumption but high peak consumption

You need an “inverter drive” fridge. It’s effectively soft-start and stays on continuously instead of justt a binary on/off.

Many options available at the consumer level.

Dunno if it gets angry if it senses that it’s browning out its own circuit or just reduces its draw (vs increasing current draw). But does mean it can dial up and down its draw on a continuous basis.