There is more to value and cost than money.
I often wondered why Dave Ramsey wasn't more popular with HN, he promotes starting businesses like a startup needs to start, work on the side, build your business logically, work your tail off and run LEAN (though he goes a little further and says pay cash for everything).
If you live in a city with great public transportation, an annual pass will cost about $1200. Taking taxis and renting cars to fulfil those other trips won't add up to much. You can save even more money this way and go green at the same time :)
In SF, a transit pass costs $60 a month for an adult. I probably spend $60 a month on Zipcar (at most), and maybe $30 on cabs. So that's $150 a month on transportation. When I lived in Seattle (a cheaper place than SF) with my beater car, I paid that in auto insurance and parking alone. Even though I didn't drive that much, I was easily spending $300 a month on the car.
I've done this for over a year now, and I really don't miss having a car. Services like Zipcar really make it convenient for those rare occasions when I need a vehicle. The rest of the time, it's incredibly nice not to have to think about it.
I just spent a year and a half without a car, and it was a nightmare some weeks. It basically means no spontaneous trips unless you happen to have an extra half an hour to get there, on average. Oh, and the choice between spending several hours a week grocery shopping (mostly in walking to and from the store) or paying 15% extra to have most stuff delivered isn't fun. I think if you put an hourly price on all the inconvenience, a car comes off as the less expensive option.
As always, you need to look at your life and make the appropriate choices. I spent many years without a car and I look back to it as a good time. The trick is to look at things globally and then not sweat on the small expenses (like the grocery delivery charge and taxi fares) if they were budgeted as a way to afford bigger costs.
Ultimately, that's the choice, yes: is it worth having a device to avoid having to plan your life around not having it.
The problem exists even if you have a car but live out of town.
That's true. The difference in rent/mortgage is important there, though. In reality, the car I bought last weekend will not cost me anything like 10-12K over the next year (2K for the car, 1K for insurance, 1-2K for gas) unless it has terrible repair costs, but there's an upper limit of 2-3K on repairs before I just buy a different car. Now, if you're paying $500/mo plus insurance and drive it 50 miles to work every day, it might be different.
But 25 minutes (10 each way and an optimistic 5 to get something, wait in line, check out...) is too long for this use case anyway, in my opinion; it's just barely possible with a car, and I live about 12 minutes walk or 3-4 minutes drive from a store right now.
Otherwise, I agree with you in principle, but living in a city with great public transportation isn't an option for everyone.
As for the original analysis, the point where maintenance costs exceed the value of the vehicle is irrelevant. I typically drive cars way past the point where they're basically worthless; as long as the maintenance costs are under a couple of thousand a year, I figure I'm better off than I would be buying a replacement.