"I don't know what used car prices are where you live, but that doesn't sound like realistic advice where I live."
You can buy a 2017 Honda HRV today for $14k, It won't be worth more than $10k in 3-5 years I guarantee it. If you maintain them properly most cars are reasonably reliable for 10-15 years. There are plenty of cars that fall in that price range after haggling.
"Abusing the mileage? What's that? Most people put most of the miles on their vehicles for their jobs. Most of mine is commuting to work and back, with some for going to stores and visiting close friends and relatives. I'd be hard-pressed to cut 10% off my yearly mileage and still work and eat."
Abusing the mileage would be frequently using it for long range transport. Typical lease limits are a fine high end for most everyone 12-15k/yr. That is what planes, trains, and buses are for.
"Alternately, focusing on low TCO means not buying insurance on the car itself, so if you're in an accident and it's ruled largely or all your fault (and these things happen), you suddenly need to get $8-$10K to buy a new car."
I fail to see how buying insurance significantly impacts the TCO of a car you own and didn't pay for vs a car the bank owns and depreciates about 10%/yr for the first five years.
"I paid a little under that for a new car, on a four-year zero-interest loan. After three years, I will have paid off 75% of the principal, and the car will be worth a lot more than $8K, so I won't be underwater."
No, zero interest is effectively the same thing as paying cash. I take 0% whenever I can barring any fees and then readjust what I pay so it actually pays everything off in time since they are often tricks that become deferred interest if you make the payment asked for. But a car you buy used for 8k is still worth about 8k a year or two later. That brand new $35k car will have depreciated by 8k within a year or two.
Repairs are a thing but if you maintain a vehicle and it isn't a rental or salesman car they are uncommon until you get in that 12-15yr range. Trying to make you think used cars which have been taken care of are breaking left and right and completely unreliable is partly true in that not all vehicles has been well cared for, also a factor for long drives and roadtrips that aren't really in fashion here in the states anymore, and the rest an argument used to help people feel good about spending way too much on something that doesn't get you to work any more successfully than the cheapest car in the lot.
Cars are liabilities not assets, sound financial planning is to minimize liabilities.