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Why is it not easy to store electricity? What about some deep cycle batteries and some controls to restore and release it later? Doesn’t seem that hard.

It's a matter of cost, weight, space, and practicality. Sure, you can hook up a couple batteries and a charging system, but how much do you really need? A single car battery can power a fridge for about 8-12 hours, BUT that depends on several factors. Car batteries aren't good at long slow discharges. They're designed for a big burst to start the engine, then get recharged. Constant discharge under 80% will kill your electrode plates quick. Marine batteries are better for this stuff, but still not great, only supposed to discharge to 50% or so. Real deep-cycle batteries are what you'd want, but that means $$$.

- Auto battery: $50-150
- Marine batt: $100-$250
- Deep cycle: $200+ (real industrial ones can hit a grand or more)

You'd need a good inverter that can handle a clean power output (pure sine wave), and has a max wattage that can handle kicking on the compressor. Couple hundred dollars for this guy. You need a control system to handle charging up during the day, and power out at night. And when to switch to external power if the system zeroes out. No idea on this, but I would guess a couple thousand. Maybe Upper/tens of thousands if you have 240V for AC or any other fancy stuff (5wire maybe).

Assuming you have a couple fridges, lights, fans, you'd probably want two batteries worth per large appliance for an overnight charge, and an even more powerful inverter, both for maintenance current, and if multiple appliances kick on at the same time. I have no idea on cost, maybe a grand for it? And 6-8 batteries now puts you at $1000+ as well.

Where is all of this going? The garage likely? Now you're losing at least a water heater worth of space out there. Plus, how much is all the wiring to run and install the system? Hopefully you have space close to your breaker box for it all (and the box isn't in your master closet or outside on a random wall). You probably want a cooling system with all these batteries and power discharges. Some kind of emergency auto-fire suppression mayhaps?

Avoid using the microwave on battery power, those things have huge power draws that most people don't expect.
Make sure your AC is turned off, those can pull 3-4x your normal power consumption, and generally need to have 220/240 volt input. And can pull 3-5000 watts when starting up.
Likewise, turn the heat off, unless you have a gas system. Little space heaters pull 10-15 amps, so one of those would drain your system pretty quick.

So, overall, no, it is not that easy to just store the power. Takes quite a decent amount of gear to legitimately wire your home for this, and several thousand, if not tens of thousands, of dollars. Not something for the average Joe. You'd be better off (if emergency power was your goal) buying a 7500W generator for a thousand bucks. Or, just for the fridge get a smaller one for a couple hundred $$. Much more portable system, plus to recharge it takes a minute to dump fuel in, and can be done at night, on a cloudy day, anytime really. Much easier to store electricity in a fuel can than from a solar panel.

Yes, I understand. I'm thinking that IF someone is installing a major solar system that what you describe would be calculated, charged and installed along with it. Therefore the blanket statement that it's not easy doesn't sound right. It's expensive but it can be done so why just toss that idea away?

I did some research 15 years ago when I was thinking about a combination of wind and solar - in my mind I would have built a cement block battery shed cooled in a few ways; shaded, roofop wind turbine vent. I have one right now that works pretty good on the shed and that doesn't even have shade.

- Deep cycle: $200+ (real industrial ones can hit a grand or more)

Each. I have 10 of them, and that's barely enough to run a few appliances. The other thing you need to mention is whether the batteries are sealed. The $200 batteries are AGM and sealed. Auto batteries and many marine batteries are not. That means they need to be in a venitlated space.