It is very true what I stated, and you are correct in your assessment. Obviously you have to compare apples to apples in terms of KWh comparing generator vs PW. The cost is not even comparable. A 22KWh Honeywell/Generac from Costco goes on sale for $4200 time to time. I bought one had it ready to go but my solar company convinced me to go the battery route promising the AC will work. The PWs more than double the cost after rebate and tax credit. Only reason I opted to go the battery route personally is in Cali there is quakes, if they shut the gas down than you are out of luck unless you have propane backup and that is not an option with HOAs.
All the 20KWh+ Generators come with a ATS designed specifically to handle AC inrush loads, a soft start built into the transfer switch. That generator would have ran the whole house with AC no problem and more and it cost less than one PW.
Again people need to do their own due diligence and not fall for the sales pitch no matter what Tesla or anyone says, same with Generators, there is some minor maintenance like oil changes and valve lash adjustment, if you are handy it's not a big deal you can do it yourself or pay your installer. At the end of the day there is trade offs. If you have the luxury of buying either for just emergencies which was my need you have to honestly ask yourself several questions about the use case and look at the pros and cons.