Yes, I think raising the minimum wage would be a good idea but I also think MASSIVELY simplifying our Orwellian tax code (both corporate & individual) while lowering the corporate tax and lowering the marginal rates for individuals are a good ideas also. Not exactly related, but could be politically possible to both labor and business oriented political actors but we can't get anything done anymore so put that in the snowball's chance in hell column...
National policy can not be solely on what is beneficial to certain business interests, we had a war about this around the 1860's or so... there was a labor system that made a lot of people very rich directly by producing a commodity very cheaply and indirectly by supplying that commodity cheaply for production but we decided as a nation that it was not right and we weren't going to allow it anymore.
Your right money talks and people flock to the cheaper option but does that mean we should allow:
Goods produced by slave/child labor and/or sweatshop labor?
Counterfeit or stolen goods produced and supplied illicitly?
Goods produced from enemy nations to be freely traded in our economy? Should we allow Iran to directly supply the US energy market?
Why do we control commerce and business on the national, state & local level? Should we let toxic waste dumps be put in the middle of low income neighborhoods because the land is cheaper?
I also have to take issue with your idea that a genocide is required to secure the border and that it would be unbelievably expensive. Israel built a 143 mile fence system in two years for a cost of $377 million, it works and has dropped illegal crossing from 14,715 in 2010 to 36 in 2013 for the same stretch of the Sinai. We don't have to fence nor should be fence the entire border, we need only fence the adjoining urban areas, road crossings, and patrol with a combination of Federal & State LE in areas adjoining those areas, let the National Guard patrol the remote and wilderness area. The cost is not so great we can not afford it and it DIRECTLY adds to the security and sovereignty of the United States of America by keeping people out that are attempting to cross into it illegally.
The combined cost of the CBP & ICE is $18 billion, that is equal to 2% of the entire DoD budget. It cost about $400K for every soldier to support & pay on average each soldier during the Iraq War, this is just a WAG but even at $200K per year to support & pay a soldier on the border, you could have 10,000 National Guardsmen for $2 billion or 0.2% of the DoD budget. That would average 5 soldiers for every mile of the 2,000 mile border but coordinating them with CBP, you have for a small cost in the overall scheme of things, actual boots on the ground in sufficient numbers to be in control. The ground and air support could average to $200K per soldier and you would still be spending only 0.4% of the entire DoD. Just to take another WAG at a part of the possible air support piece, you could have 25 MC-12s deployed to the border patrol mission, flying a 6 hour mission per day at a cost of $1,500 per flight hour (WAG) and cost $82 million per year for good ISR support, that is chump change in terms of the DoD budget and it would saturate high traffic areas with ISR to enhance your ground forces. Again, this is affordable, it is possible and it is what we should be doing.
A border security system that is designed and funded to be effective does nothing more than stop illegal activity, if you have a problem with our labor & immigration laws then try to change them legally. Do not advocate for allowing illegal alien criminals, because they are criminals, to be allowed to keep committing their crime(s) by confusing the argument (whether or not we should defend our nation, enforce our laws and assert our sovereignty) by raising the red herring and emotional argument of it is cheap labor that benefits some businesses and individuals as being in some ways economically efficient so therefore, screw it let's allow it. The almighty dollar is not the end all be all of our decision making, it is a balance of what is right, prudent and in our long-term interest.