as i've said before, raising the minimum wages doesn't "fix" anything...getting people to invest in themselves (through a trade, higher education, etc) and have them earn a better wage is what benefits everyone.
So we're going to have a nation of well educated, well employed people? Sounds awesome. But, who is going to work at McDonalds or Timmies or WalMart? We have huge numbers of those service jobs and I doubt we can send all those folks into trades or higher education as many of them simply don't have the ability, and the economy can't adjust to having hundreds of thousands of people leaving the retail industry.
Your vision works well on a micro, individual level, but fails on a macro level.
Low minimum wages are hurting the US. A company like WalMart or McDonalds takes advantage of the high unemployment to pay low wages. Those two companies in particular are not just scraping by and have to pay people poorly. They make hundreds of billions in profits. They could easily raise their wages and not have to pass along one penny to consumers.
The real killer is the costs associated with low minimum wages. The costs to everyone. Those folks at WalMart earning $7,25/hr have to rely on government programs like food stamps and income assistance. Tax payers are providing hundreds of millions of dollars in subsidies to massive companies that are hugely profitable in the form of transfer payments to low wage earners.
It is detrimental to the entire nation to have the minimum wage so low that we have people earning less than a subsistence income.
The cost of living is high in Oz and for many reasons, not the minimum wage. Small population, little manufacturing, little exportation of resources or goods, no vast energy resources, and on and on.