You can size your unit to the load that is necessary.
If you have a 5000 sq ft house and place a 15 KW standby, you must decide what load you want placed on that generator You can runs lights and your refrigerator, or maybe lights and one central air conditioning unit.
You can isolate the load to that generator.
You must size the load not according to the whole house but to the load it serves.
If you want to run lights, then you must be able to run the lights.
If you start the generator and it dies, then the unit is not capable of handling that load.
A generator must be capable of starting a central unit and handling that LRA (Lock Rotor Amperage) of that unit.
You can get a smaller generator but it won't run your whole house especially your central air conditioning unit or your heat strip.
When purchasing a whole house generator, you must consider the serge amperage that happens with motor load equipment.
Motor load equipment would be your refrigerator, microwave, well pump, garbage disposal, washing machine, dryer, and dishwasher.
A serge capacity is for 3 seconds.
I have a generator that advertised handling 6500 watts.
That generator does not carry a load up to 6500 watts.
It carries a load of about 4500 watts and will serge up to 6500 watts for 3 seconds.
When purchasing a generator, you must be aware of the surge capacity.
For instance, look at a propane verses natural gas generator.
A propane generator is rated higher.
An advertised 16 KW might actually run as a 14 KW if you want it in natural gas capacity.