Re: No Backup Gen?
I think the limiting factor with Powerwall (and other similar tech), is the batteries themselves, rather than the inverters. I know Powerwall 2 can, as you mention, do 5kW continuous, but that is per Powerwall. So if you needed more than 5kW, you could install additional Powerwalls and so get 10kW, 15kW etc. More cost though!
One Gateway 2 can manage up to 10 Powerwalls, so that's a potential 50kW continuous. (Probably £70k+ install cost!!).
I think there is some re-education to be done as well. I've had solar for a few years, (no battery) and got into the habit of only using the dishwasher etc during the day, and never at the same time as doing laundry. But obviously this wouldn't always be an option for everyone, and I still use the electric oven in the evening, which means it's dark at the moment (UK).
If I do get a battery, the timing can be more flexible then, but I'd still be trying to avoid doing too many high Watt jobs at the same time.
Interesting on you only having an 80A supply fuse, I've just double checked, and both my main breaker in the fuse box, and the fuse on the feed into the meter are 100A.