To deal with blackouts there's a whole lot of real-estate between lighting a couple of candles and a totally automated 10-15kW whole home natural gas/propane generator that's plumbed into the gas source and wired into your home's electrical - and so there are a lot of different solutions for different budgets and needs. This thread was started about using a smaller gasoline generator to recharge a battery based power station ... and that's the "design" that I'm talking about.
Home electrical loads are not in any way a steady state load. Fridges, freezers, water pumps, microwaves, air conditioners, kettles, hot water tanks, etc. all come on and off at different times producing mutli hundred or thousand kW swings in the loading of any power source. ICE generators are hugely inefficient (fuel usage wise) when powering variable loads, they are much happier running at a steady state (rpm and load). Batteries on the other hand simply don't care about the loads if used within their design specs. Plus who cares if there's an extra step within a battery power station to convert AC to DC back to AC (with the few % point loss with each step) when you're comparing it to an ICE design that't maybe at best 30% efficient in turning burning hyrdocarbons into electrons. If you are dealing with a multi day blackout having an ICE generator plus the battery that uses one gallon of fuel a day vs two or three gallons without the battery is a big advantage. The idea is to size the power station (in kW) for the peak loads and then to recharge it multiple times to break the day down into smaller chunks so you don't need the total battery capacity (in kWhr) for the whole 24hrs. Now the battery can be 2 or 3 times smaller (and much less $) when you use the ICE generator to just recharge it. If you are buying the two things new the ICE generator can also be smaller since it only has to be sized to recharge the power station and not handle the peak kW loads.
When sized correctly the battery power stations are just as happy putting out a few hundred watts to power just your lights and TV as they are when the fridge's compressor kicks in and draws many hundreds more. ICE generators vary in rpm as the loads change (assuming that the new loads are above a baseline so this is much more noticeable on smaller generators). As the ICE generator changes rpms the frequency of the AC output changes. Ever put an oscilloscope on the output of a generator and varied the loads? Yes It's a sine wave, but an ugly one ... and often also very clipped and choppy with the smaller generators. This is why there are cautions and warnings on the usage of many less expensive ICE generators with "sensitive electronics". They work great with steady loads that are not anywhere near their rated capacities, but load them up and they use a lot more fuel and put out very dirty AC power.
This is where the battery power stations come in. When used to only re charge the power station they isolate the variable loads from the generator and any dirty AC from the household appliances. You're absolutely correct that they are also more expensive than just a simple generator but they provide a wide variety of additional benefits plus they're constantly coming down in price as battery technology evolves (an area where around the world more $ and manpower is currently applied to than any other power technology). Mid sized (1-4kWhr) power stations are currently priced in the 1.5-3 Whr per dollar (USD) range and are virtually all using LFP battery technology (nobody in this market of portable sized power stations uses LiPO any more - but that's still offered in the whole house setups like Powerwalls, etc. ... for now).
I heard an interesting comment about batteries the other day ... Our modern world is in a constant state of energy usage that comes in constant peaks and valleys. Warmth, cooling, cooking, transportation, etc. are all delivered in those peaks. However we're also much more efficient (in delivery, cost, generation, etc.) when we deal with energy in a steady state. There is simply nothing in our world these days that does a better job at creating that steady state of energy for all of our different needs than the rechargeable battery.