If one lacks the rainy-day savings to afford a hypothetical thousand-dollar repair bill, one certainly cannot afford to throw away thousands of dollars every year “to not have to worry” about one’s precarious finances.
There are plenty of people who live near paycheck-to-paycheck who also need a car to get to work, where a stroke of bad luck like engine + transmission damage would not only be a significant financial hit but the downtime of the car being unavailable might compound the problem as they can't get to work.
While it's not a great financial situation and ideally nobody should be in it, in reality these people don't have a choice and budgeting away a fixed percentage of their salary on a vehicle that guarantees them to be able to get to work (to pocket the remaining percentage of salary) is a better option than not paying a monthly fee but gambling on the fact that a significant breakdown might completely wipe them out financially and jeopardize the transportation they use to get to work.
It's a bit like insurance - technically it should always be cheaper to self-insure, but insurance exists because for many people perpetually paying the premium is still better than a single event wiping them out completely.
This makes sense so long as it isn't used as an argument for leasing a new car on an ongoing basis. If one actually finds themselves in this situation, the responsible approach would be to find the cheapest possible lease and to save aggressively until they can take the more economical approach.
Leasing is like credit card debt. It makes sense in some rare cases, but in most cases it is wasteful and the average consumer should avoid it.