For households in Europe, there are some incentives to switch to heat pumps for heating... for best efficiency (and longevity), usually a heat pump needs to run at lower power constantly without switching off much.

And since the heat pump will be the biggest total consumer in a household (in winter), there is not a huge opportunity for flexibility.

This seems like a sort of complex trade-off (taking your word for it that they do run more efficiently when run continuously). We’d still probably prefer to run them on renewable energy and defer them when running on non-renewables, because the inefficiently consuming a plentiful resource that is not very damaging to produce, is better than efficiently consuming one that is destructive to produce.

But if we have multiple tasks with multiple levels of defer-ability (either due to efficiency benefits or due to people just wanting to run their dishwashers at a time convenient to them), it could be more complicated. But working out trade offs like this is what the market is for, right?