How many people will turn off AC and will not bake that cake, or wash clothes, when they know they're going off their own battery vs some electricity distributor's battery shared by others?

And if someone is dumb enough to do high load stuff on their own battery during a blackout, then it's less of a problem for others. Also individual failures will cover less homes.

Incentives and consequences will be different and differently spread.

And on individual level, you can also chose whether you want this or are fine with outage. (I'm against mandating this)

Not if 1 million people install and monitor them instead of 100 people.

100 huge batteries are going to be monitored and maintained far better than 1 million.

Given how the average consumer monitors, maintains, and secures their home PC ... this is a level of assurance we want to put on the power grid?