You cannot depend on the Sun for backup, especially in the Winter when you are most likely to have a power failure and when you need the back up the most.
Looking at December. Notice how there was a whole week of no production.
Why was there no production for a week? Probably because the Solar panels were covered in Ice. The same Ice that knocks power out.
The Red is consumption. Green is Production
The Sun drastically reduces in Winter. Check out December and January.
This was a very light Winter too.
Batteries are great for short to modest power outages. They are instant. And might last you 1-2 days. And the chances of you charging them back up from a Snow or Ice storm that knocked power out is fairly low. Even if the sun is out and panels clear they will charge very slowly in winter.
You're talking about $30K for Solar + Batteries (depending on size) and it still might not cover you for an extended power outage. Which is rare, but happens.
A full standby generator would run indefinitely, be much cheaper and just as convenient. Assuming you have or can get fuel for it.
I love Solar, I have solar. I love the Battery concept too. But batteries for backup just don't make financial sense. Batteries are great if you are on Off Peak Metering. Batteries are a luxury if you have money to burn. And let them cover short to medium power outages. But for power security you still need a generator unfortunately. If you don't want or need 100% power security and can afford the Battery setup. Go for it. Batteries would also be great if you had lot's of short power outages.
On average people use about 20 kWh a day. One Tesla Powerwall (about $8000.00 installed) can supply about 12.2 Kwh. That's why most installations install at least two Power Walls.
Other battery backup systems might be much cheaper. But using HALF a normal load (say 10 kWh a day) you could go ~2 days on $16K worth of batteries.