You are spot on and installing the battery backup system does come out of pocket and it is not cheap.
If it can supply 95-100% of your power needs, then the payback time is reduced to between 10-15 years.
Some things a lot of solar companies do not tell their customers:
1 - the panels should be washed every year. They collect dust and dirt and become increasingly less efficient.
2 - solar panels are more efficient at cooler temperatures, not high temperatures. So, combining temperatures with hours of sunlight, winter is least effective, spring & summer are most effective, and summer is good because the hours of sunlight compensates for the high temperatures.
3 - You still have no power during a power outage of the grid, because you have no battery backup. This makes some sense at night, because the panels can't produce power without light. But, because ,in most cases, the power from the panels is going to the grid, not to the house, when your connection to the grid is lost your power is lost.
4 - As you mentioned, CarlS, the solar company now has a lien on your house, so not only does it raise the cost of the house when it goes up for sale, the house can't be sold without the agreement of the solar company.
I am not saying it is a bad idea, but the consumer NEEDS to be informed. In principle, I support solar power, I just wish they could improve the efficiency of the panels, which has not significantly improve since the 1980's.