There's a huge difference between someone leasing or buying a new car every 3 years, and someone keeping a car for 10-15 years. The latter can spend 5x as much on a car and end up in about the same place.
No they can't, a person can afford a certain amount of car payment, buying or leasing doesn't impact the amount of car payment they can afford. In fact they can afford far less car buying because their payments will be much higher. AFTER the car is paid off they will start saving money but that has no impact whatsoever on how much car and what payment amount they can afford.
A person can afford a fixed amount per year, the more you make and the less debt you have the higher that amount is, keeping the car after it is paid off doesn't affect that number and doesn't increase the amount they can spend. A person that leases tends to pay only about 50-70% of what it would cost to buy the same vehicle over the same amount of time, they can either get a more expensive vehicle for the same monthly payment or they can have a lower monthly payment for the same vehicle.
For example our Edge with zero down costs us $400 a month to lease for 39 months, cost of ownership is $15,600 for the whole term which includes all maintenance. Financing the same vehicle for 39 months at 2% would be car payments of $983 per month, more than twice as much, even a 72 month loan at 2% is $547 per month. The person that finances for 39 months will pay $35,388 or $19,788 more than the person that leases for the same term.
Someone that buys a car and pays it off in 39 months has to keep it 48 more months (a total of 7 years) just to break even with the guy that's leasing. At that point the guy that's leasing has leased and returned another car, the leaser has paid less and is on new car number three while the buyer is stuck with a 7 year old car.
Also the guy doing a 39 month lease usually doesn't have to pay for maintenance, doesn't pay for tires (mileage is low enough they don't need to be replaced most the time), and doesn't have to worry about mechanical failure. You also only pay sales tax on the portion you lease instead of the entire vehicle which can be a good amount of savings.