I think you misunderstood what I said.
I made no claim that $7.25/hr is a livable wage. That is the current federal minimum. Employers are required to pay the minimum, if they aren't, they're breaking the law.
Money management is certainly no silver bullet, however, it plays a role. If you net $13k/year then you have to manage that money so you don't spend more than $13k/year. Most would agree that it is extremely tough to live on $13k/year. No matter the difficulty the money still has to be managed.
In my student loan example, if you have a loan schedule of 30 years @ 6% you will pay $46k in interest on a $40k loan when only paying the minimum of $240. That same loan if paid off @ $440/mo, nets you $33k over that time period. Here you would manage your money so that you can pay as much as possible on that loan as often as possible.
Making more money doesn't solve money issues, it just covers them up. Saying that there nothing to be done because the amount spent is greater than the amount earned seems rather foolish. I'm not saying that in any given situation there exists an outcome where you can manage spending less than you earn, but managing money wisely will always improve the situation.