I looked up both my low cost birth county in Montana and my current high cost home county in Washington. Both had a budget of about $5,000 a year for transportation. Which, ignoring all maintenance, fuel and registration costs would leave you with about $300 per month after meeting most state minimum insurance requirements and full coverage. That's the payment on about a $15,000 car financed over 60 months, if you have good credit. Not a beater by any means but honestly that's pretty much the value sweet spot in terms of getting a reliable used car. You could get more car by ditching full coverage but as Dave Ramsey says, "you insure the things you cannot afford to replace." Your sole mode of getting to work seems like a thing you probably can't afford to replace on minimum wage. Again, you can play with the numbers but I already threw your argument the bone of ignoring, fuel, maintenance and licensing costs. A nontrivial sum.
Regardless, I'm not sure why your argument takes as it's premise that a living wage should represent the minimum a person needs to get by in our modern world. Why is that the default standard?
Edit: When I think about it more, isn't that kind of the whole point of a proposing a living wage over a minimum wage? People proposing it believe that we shouldn't peg wages to the minimum a person needs but rather to some fulfilling standard of living?
I think it depends on what we intend on doing with living wage as a measure. Typically I see it called out as a safety net minimum for what people should make. Frequently mentioned as a floor for minimum wage talks.
So if it’s a baseline then it should be the minimum. If It’s some median target then that’s different.
I don’t think it’s useful to have a median target because it’s so arbitrary depending on individual circumstances and desires.
The calculator is pretty strange, though. A quick glance under the hood reveals that the calculator goes well out of its way to inflate the cost of living which is used to calculate the 'living wage' in a given area. They consider a mobile phone as a basic need, which makes sense. But when they calculated the cost of a mobile phone, they included the price of a new $200 phone every 2 years, and a plan that includes 10GB of mobile data per month! As a result, the expected monthly cost of a phone was ~3x what I pay. When pricing broadband internet, they said $60/mo was the lowest they could find in my area, which again was ~3x my own monthly expense. The transportation allowance was so high as to be roughly equivalent to the payment+insurance on a 1-2 year old Toyota Corolla. For the food allowance, they arbitrarily chose the 'second cheapest' FDA approved balanced meal plan price scheme, which added $60/mo in expenses for no reason whatsoever. That's where I quit investigating, but I would be surprised if those are the only living expenses which were so inflated.