These calculations often fail to account for present vs future value of money.
If you’re financing the system you have no big cash outlay, but returns are further out, possibly never when accounting for the useful like of the system.
With cash up front all the returns are yours, but they are much lower than what that cash would net you in an average investment.
The financial math on small solar systems can be complex. If the system is sufficient to provide power to major appliances in a power outage (assuming you have a power outage risk in your area), it can make more sense to tie money up in these systems.