Yes, I did write, the power!
It's not about the daily amount of energy, but about how much energy the devices use per second!
If the system can provide 625 J (joules) of energy per second, but your washing machine draws 2000 J per second, then you have to buy 1375 joules every second, or the washing machine won't run! Many household appliances (including dishwasher, refrigerator) work in such a way that they require a lot of power in intervals. So the combined heat and power plant can only serve the base load, or low consumers like lamps, standby operations, etc., but if you really need power, that's not enough.
As a comparison, your water is delivered drip by drip, 200 liters of water per day (an average calculation showed that this covers your annual water consumption).. The only problem is if you want to shower at 5 in the morning and then stand there dry..
(too late--- but combined heat and power plants are complicated anyway)