Considering the retail cost of 100W and 200W solar panels, an 8-10KW inverter isn't THAT expensive and neither is an array of deep cycle marine batteries. Now if you want something like Tesla's powerwall that's going to cost quite a bit more.
I don’t understand what your trying to get at here.
Is it expensive to build an off-grid solar/battery system? Depends on how you are looking at it and if you are willing to adapt your lifestyle to it or not.
You need more in solar capacity (kWh) than you use in a typical day to go off grid and have it be sustainable. Since solar only runs for about 30% of the day at or near full output, and you need to run your home ~and~ recharge your batteries in that time, multiply your kW size requirement by a factor of 4-5 to get what you need in solar sizing.
A typical home with typical on-grid use patterns use will need on the order of 10kW or more of solar panels. If your willing to adapt your lifestyle, watch how you consume energy, time high/load activities with solar output, monitor and minimize battery cycling - you can get by with less. A single person on a very disciplined power budget might be able to get by with <1000W in panels - but that isn’t typical and it would be a pretty spartan power budget.
Also consider even with deep cycle batteries, your going to have to replace them periodically. About 5 years is average, 2 years isn’t uncommon, you might get lucky and get 7-8 years if you baby them. And your going to need more than 3 or 4 of them if you want to keep things like your fridge powered all night long. Off grid battery systems, to get enough storage to run all night and have decent lifespan, is typically a few thousand dollars worth of flooded lead acid deep cycles. Once you take into account the cycle life and amount of overprovisioning required to keep a useful lifespan and provide peak power/current - that’s where LiPo starts to give a better return than lead acid, even though it costs a lot more up front.
If you get a Habor Freight $199 10kW inverter, don’t be surprised if every appliance in your house starts to burn out on regular basis, or eat a set of batteries every 6 months. A quality off grid inverter, that can handle battery charge Control and utility grade voltage and frequency regulation is going to run about $4-6K for a typical house size (4-10kW).
Unless you really like that RV/camping lifestyle, it costs a good bit more than you would expect to have real, reliable off grid power. For nearly everyone, the utility rate is a pretty good deal. The only reasons solar is financially competitive are incentives/rebates, and Net Energy Metering. You take away either of those and solar all of a sudden has a very long payback compared to utility rates - and that especially includes off grid solar, as it won’t get NEM and has reoccurring storage replacement costs.