TLDR depends on the efficiency of the fridge. You’re right of course though - I edited linked comment to be more conservative at 2-3 days also. I can get my personal lab fridge to last 5 days though (110W power draw, once every hour for 5 minutes). :P
If your outage is longer than expected, the battery will recharge in a little over an hour and be ready to go again (if the grid comes on for a bit, or from your generator, a neighbor's etc).
Hmm ... "Stores power from your generator" might be a market with room here since generators are often inefficient (and produce weird power) and batteries have grown a lot lately. OTOH, in practice home generators are more limited by "how often do we need to (and given the state of the infrastructure, can we) go buy a new can of gas" than efficiency. And even if efficiency does matter, how long will it take to pay off?
Practical problems we had the one time we actually needed our generator were:
* (remember to turn off the main breaker)
* whoops, we blew the GFCI when we tried to back-feed power through an external outlet, so we had to run an extension cord through a door (with all that implies). This is the only thing that actually took us by surprise and took some debugging in the weeks following.
* the 120V generator only one half of the split phase, so every other circuit in the breaker box doesn't work. Pick your half carefully!
* the generator is strong enough to run normal appliances, but not the well pump (note: we had a completely different plan for heating). Here I suppose a battery could've been useful ... but then, the reason we didn't just buy a bigger generator in the first place was cost (for an extended-outage event that only happens once in multiple decades; for anything shorter you can just ... not open the fridge).
* (just a note that with the increasing electrification of cars, some variant of "plug your house into your car" is likely to become more of a thing)
While I've seen the grid flicker, this has only ever happened just at the start or just before it comes on permanently, so I'm not sure how useful it is to consider the "comes on for a bit" case either.
If your outage is longer than expected, the battery will recharge in a little over an hour and be ready to go again (if the grid comes on for a bit, or from your generator, a neighbor's etc).