Nope, not even close. Gas is at least double what you’ve estimated, and I would add at least another $300 for groceries for a family of four (the lowest USDA estimate is $1k a month so that’s still lowballing it). Say another $100-ish for car/renters insurance, $50 for internet, another $50 for a budget phone plan and that’s your $4k take home gone before you even get to any other utilities, healthcare, car maintenance, toiletries, etc. They’re not saving for retirement, they don’t have health insurance, and they definitely can’t afford to do anything fun. Your hypothetical family is not breaking even, they’re in the red each month as a baseline and, like most Americans, they’re one emergency away from financial ruin.
Literally all the data is against you on this one. I’m not sure where you’ve been getting your numbers but basic living wage for a family of four in your county is estimated at $91k according to the MIT data, and that assumes one of the adults is staying home with the kids - if both work it goes up to $115k. A single person with no kids would need $50k just to “make ends meet.” The fact that people technically can survive on less (by taking on debt and putting off basics like healthcare and retirement) doesn’t make it affordable or sustainable.