The Ignorence of a Minimum Wage Argument

Today there is so much argument for raising minimum wage and any time now, it could happen. However, I think that there is invalidity in the arguments used to raise minimum wage. I look out for the poor. But I do not feel as if the poor are helped much by raising minimum wage. Of course, I don't think that there will be a huge fall in the economy if it is raised to just over $7 an hour because most people are making at least $7 an hour anyway. The largest amount of those who are not making that much is high school students, retired men looking for a little extra money, widows, and wives looking for a second income (particularly the first). Sometimes they even make more.
In general, I don't feel it is the government's responsibility to set up a minimum wage. If they set up a minimum wage, why not a maximum wage to "protect" the employer? A wage is an agreement, and either side has the "legal" right to walk out of the deal for any reason justified or unjustified. This is not at all the government's responsibility. What makes the worker a better person than the one who hires the worker?
Beyond this, I don't think it is good for the economy to have a minimum wage. The only good benefit I see is that it balances work for well-to-do Americans and those who are not well to do, or maybe immigrants- not neccessarily legal or illegal. But this goes to help the rich and middle class- not the poor, right, because the poor are willing to work for less because they are more desperate. They may be helped to, to a degree, but it also gives more jobs to the well-to-do, richer Americans.
It sounds like I am trying to build a case for minimum wage, but I am not. It is not the government's job to control wages like this. I certainly don't think that minimum wage creates jobs, since that means more money for businesess to pay. It probably looses jobs, if anything. Therefore, if the richer people are getting more jobs due to minimum wage, it must really take away jobs from the poor. Of course, Mexicans are part of this side that are hurt, and Americans may like that, but the government's job is to protect the border from illegals, not making it illegal to become legal, and then work for money. The very argument used to support minimum wage can be used against it as well.
So if minimum wage wants to help the poor- it will probably fail. Think of it like this: Three uneducated, inexperienced, poor people want a job. They are uneducated, inexprienced, and poor, so they are not as efficient as an educated, experienced, rich person at the job. The rich person can do as much work for a given amount of time as the three poor people can altogether. Thus, the worker can pay three people "x" amount a piece, or the one rich person "3x" for him (x being a given payment). He may, to be nice, decide to help the poor people out and give them a low-paying job, and let them gain experience, and then get better benifits. He may, then again, choose to get one rich person to work with. The chances of him hiring the poor people is theoretically 50/50, but to give them a job, from the kindness of his heart, he may hire them.
Now let's say that a minimum wage of $7 per hour is put into place. It seems good that the poor get the job, and now $7 a piece (we'll assume that that was more than the given "x"). But the employer will probably rather give $7 to one rich person instead of three amounts of $7 (one to each poor person). They both work an hour, and in a way, both as hard theoretically (the poor may actually work harder working on skill improvements for the job), so the person wants to hire the rich person to save money for the job. Beyond this, he must now pay the rich person mroe money because the rich person's wage was three times as high as the poor people's wage was. Now, $21 exceeds the "3x" he was getting paid. He raises himself to $18 to get more money, and to still get the job. They employer, following his own motivations, hires the rich person. The poor people are out of a job; the rich people have more jobs and more money; and businesess now are hurting by paying extra money. What happened to a free market? You can call it greed that the employer would not give the poor a chance after the minimum wage was in place, but it is not necesarily greed- it is following one's own desires- I do it and I imagine you do it when it comes to money. What's next, is the government going to outlaw this so-called "greed?" It may sound good- "greed is bad, stopping it is good" but all it will be is another way for the government to get their hands in the economy and our own personal lives.
Minimum wage helps some people, but hurts more than it helps. Beyond that, it is not the governments job to give a minimum (or a maximum) of payment. Of course, the government will claim "friend of the little guy" to get our votes and gullible Americans fall for it. It makes me wonder how much minimum wage talk done by the Democrats mostly is just ignorence, and how much is hypocracy. For American middle-class citizens, it's ignorence. We do what sounds good on the surface. But for politicians, those who are supposed to be educated about the government and the economy, I think that a lot of it is hypocracy; but, then again, I'll let God be the judge of that.
What do you think?
-Ryan