Truth? That depends on your actual usage.
I can only share that my system (see signature) is insufficient for my needs during the summers. I go to sunset with my 2 PWs well below full because I'm consuming everything the sun gives me with little surplus to go to the battery. I get some battery charge, but I found myself with a continuous dependency on the grid which I was trying to move away from.
A buddy of mine that I referred to solar took a different approach. We have similar home sizes (4000 sq+), but he only has 1 PW but instead got more panels. The takeway?
His bills are more expensive. Yes he netmeters more b/c of his larger panels, but his single battery does not provide very much capacity after sunset. Net-metering provides little credit because of the delivery charges. And his single battery does not allow him to do a full house, so yes he has a 'critical load' panel which is the handful of breakers that you mentioned. For him, it was his refrigerator and I think the smaller AC unit. yes he had to work with the installers to figure this out and identify what is critical since he can't support all load. Something to think about. I get the PWs are expensive and hence I didn't get more. I actually banked on adding more later, so wanted my wiring to not make me decide now what is critical. Hell I'm banking on V2H at some point if Telsa follows the Lightning 150. They prob wouldn't to sell more PWs and solar as time passes and they can use all those batteries for cars.
Look at your AC unit's power draw and you may be able to estimate how long it'll work. Tesla said 4 hrs which to me seems like a long time on single 13.5kw capacity battery.. One of the things that I had my installers put in was a "soft start" on the AC units. The idea is 2 AC units starting at the same time would be too much for the load. So this soft-start slowly ramps up the draw to not overload.