You are mistaken.
10 kW is a LOT.
Avg use for a heavy-electrical house is about 1-1.5 kW.
Look at any stats you want.
10 kW x 24 = 240 kWh per day.
87.600 kWh per year.
Avg us house consumption is about 10.000 kWh/year, or about 8x less the 10 kW mentioned.
Of course the extra free 10 kW is only during the day, but since we get paid for the grid input whatever we use during the dusk is also essentially free.
Thats why we want to input 4-8x our use, so our power use ends up essentially at zero, or negative.
Most houses, new, have a 10 kW connection.
Ours at 14 kW, 380V 3-phase, is a heavy, industrial, unusually powerful connection.