Yeah, if you want to take it out past 5 years, you can make your own estimates. You just won't have the benefit of Edmunds' data. You are right that you will save on transaction costs if you do not buy a newer car every five years. You're also a bit of a special case in that it seems you only put about 5,000 miles per year on a car. I'd estimate your TCO on that car to be about $2K/year, which is pretty frugal. It wouldn't make sense for you to buy a new car, because you'd be losing depreciation to age faster than you'd be wearing the car out. At 20 years, you'd have only 100,000 miles on a car that would be essentially fully depreciated.
It is pretty tough, though, to get the cost of ownership on a car driven 15,000 miles/year below about $3,500/year. By comparison a new compact will be $5k to $6K per year in total cost of ownership. So if you are wondering why gold doubloons are not accumulating in the chests in your basement that much faster than they are for the guy who drives a new Honda Civic, that's why!
It's not the calculator is "wrong" in answering the question it asks, but that it's asking the wrong thing. Very few people want to buy an 11 year old car, so buying a 6 year old car and selling it 5 years later and doing the same thing again is overly penalized vs buying a 6-year old and selling it 10-15 years later (for much less), but only doing that once instead of two or three times.
> Why not compare it to a car you scrounged for free?
Because I can't repeatably find a reliable car for free. I can repeatably find many reliable cars for $8K in any city in the US. We paid $7500 for our 2005 CR-V in 2011. It was in overall great condition with high miles (165K-ish). It now has 220K miles on it and rust will kill it long before miles do (New England road salt).
Edit to add: I agree that my method above was double-counting depreciation. I should have stuck to cash items rather than including a non-cash item.