The question isn't so much how long it lasts until the engine explodes, it's how expensive is maintenance. That's the boot theory part. If you can't save up enough for the $10k car that lasts 15 years (though you mentioned a timing belt replacement and on some cars that's a few thousand $, ask me how I know...) and instead can only afford to keep buying $1000 cars, that could turn into a slew of smaller fixes that add up to a lot more than the car was initially bought for.

I'm also a bit surprised you'd buy a new car. Off-lease is much cheaper and they're still fairly new ish.