The classic definition is the wage needed to cover the basic needs of the family including things like rent

Rent where? Rent costs vary wildly.

childcare

What sort of childcare, and how many children is it meant to support? Or do you get $X per child? And if so, is there a maximum number of children, where having more won’t get you more money?

transportation

Over what distance? And how, owned vehicle or public transportation? If owned vehicle, what kind of vehicle? Used/new? Price ranges for vehicles also vary wildly.

I would go one further and say that the family needs to not be living paycheque to paycheque.

That entails what amount of extra money? And what do you do about people who willfully choose to spend it instead of saving it? Are you aware that in the US, 1 in 4 of people earning $150k or more live paycheck to paycheck? Just because one has money to save doesn’t mean they’re going to do it.

go out once in a while

Again, far too vague. How often? And how much money does ‘going out’ cost? You’d have to figure both of those out, and multiply them by each other, to ensure this goal is met.

educate their children

Taxpayer-funded public school already covers this. Unless you feel everyone should be entitled to the cost of private schooling?

save and pay for university

University tuition is another massive variable, so you’d need to decide how much is given for tuition. Also, if someone does not go to college, do they not get that part of the money?

and advance themselves.

The vaguest criterion yet. It’s pretty much impossible to say if a given minimum wage satisfies ‘everyone can advance themselves’.

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As anyone can see, this “classic” definition is still full of major holes, and not nearly complete enough to even conceptualize a goal such that progress toward it can even be measured. Just saying “living wage” over and over will never get anyone anywhere.