You are 100% correct that people cannot, today, get the panels, batteries, wiring, etc. for only $10k. To clarify, I did not buy batteries. I don't need them. The only advantage to batteries for me would be to not have a power outage when power goes out (not a common occurrence). The net metering of my utility company only charges me for my net usage (0 kw typically). Thus, no batteries and a few tax/other credits later took the $15k cost down to $10k when purchased a few years ago. I would guess that today you would need $25k to purchase what I have (still a $20k cost if you get good rebates), but I haven't researched that.
As a side note, $120/month is approximately what I save on electricity each month based on previous bills. I switched some appliances to electric from gas, saving about an additional $30/month in costs. I also have an electric car that I am not paying for gas on (savings on top of the $120 in avoided electric bills), probably creating another $100 per month in savings. While the panels will produce slightly less than needed to cover 100% of this over the full year, it gets the vast majority of it (if it covered all of it, it would be $125 savings in gas per month or about $160 with the natural gas savings). Thus, my true ROI will be quicker than the 8 years when taking that into account.
At a 2.5% interest rate over 8 years the payment would be $115/month (smaller than the $120 of electric bill savings) and this doesn't factor in the savings from deducting the interest. Thus, either way, the $1440/year in savings would still definitely on its own give me an overall positive ROI well within 10 years. Again, there certainly could be other financial approaches to create a better ROI, I have not analyzed them all so I wouldn't venture to guess on that question. But, hopefully this additional detail helps clarify how I can get a fairly decent ROI on the purchase I made.