If you really will ride 3000+ miles a year, then for sure a ping will cost less per mile than even the cheapest HK packs.
But on the other hand, if your ride is short, you won't go that far. If your ride is short, you may not need 15 ah of the cheap HK stuff.
I end up having both. I do lots of rides carrying 5-10 ah, and ping needs to be 15 ah before it will do very much. Right now I have 25 ah of cheap lico. Enough for really long rides, but most rides are shorter now. I don't need a ping now, don't work, don't commute 30 miles a day anymore.
For me, lico lasts 2 years, then degrades rapidly in capacity. This applies if you use it or not in my hotter climate. I do have some that still works though, 3.5 years old. My budget is for 10ah of new lico each spring, which should keep me going for about $300 a year in fixed battery costs. $200 a year is about what a ping costs. So it's 30% more expensive than a ping, but for me the benefit is flexibility to run big or little battery, or power multiple bikes at the same time. My primary ride would kill a ping in weeks, unless I bought 30 ah. Typical use is hauling a huge pile of groceries.
Pings lasted me 3 to 3.5 years. But they did put out a lot more wh than I ever took from the lico.
Re the savings from riding the bike, you save a LOT more than with just the fuel costs. You are on the right track to calculate the cost per wh of the battery purchase.
But the savings of not putting miles on the car is very hard to calculate. Yes, you may still have the fixed costs like insurance, but not taking that car to the repair guys, or spending your whole weekend twice a month doing your own repairs can be priceless. Very hard to calculate that savings.
For me, I made a Subaru on it's last legs continue for three extra years. Now I have a $450 a month payment on the new one all in. Then gas, if I do drive it. Trying to make the new one last forever, at 5k miles a year or less. One way to look at that savings is for that three years at least, I saved $450 a month. I sure as hell didn't have that payment added to my budget for three years.
So in three years Ebikes saved me $16000? That pov might be extreme, but I know for a fact I saved at least half that in real money I had in my pocket every weekend. $50 a week for sure, in money I wasn't spending on the car. It was there because I didn't spend it at the car parts place, or the gas station.
Of course, that $50 a week was often spent on more bike stuff.