20 kW generator overkill for a home?
You can't average the monthly usage over a number of days because the loads aren't constant. Consider the following two scenarios:


A 100W light bulb that's turned on constantly for the whole month (30 days). This uses 100W * 24hr / day * 30 day / month = 72 kWh for the month.
A 2400W heater that runs one a day for an hour. This uses 2400W * 1hr / day * 30 day / month = 72kWh.


Doing an average usage as you did, you would incorrectly assume that both scenarios need the same size generator. But, the second needs a bigger generator since the load is bigger (2400W vs 100W). They use the same amount of electricity because the smaller load is on for much longer.

Your house is similar, in that there are some big loads that run for short periods of time (AC being the biggest usually), and then there are some small loads that run for much longer (cable boxes, lights, etc). Your generator needs to be sized to provide enough power for all the loads at once.

To determine the size of generator to get, you'll need to consider what you want to run off of it. A lot of people only run a subset of their circuits from a generator to get the essentials - HVAC, a fridge, maybe a couple general receptacles. As a simplified estimate you can take the size of the breakers you want to run (in amps) and multiply it by the voltage (120V for single breakers, 240V for double) and add them up. AC units can very quickly use up most of a generator's capacity!