With apologies, I have not the wherewithal to trawl through the above two pages of back-and-forth, and nor do I possess requisite knowledge of the relevant economic calculations to counter a truly informed dissent.
Therefore, I will take the coward’s way out (although also an honest one) by saying that there is far more nuance in this debate than is generally acknowledged above.
In instances, raising the minimum wage can raise the price of consumer goods, with the simple rationale that in order to fund their workers’ wages, they have to raise prices, which leaves everybody back at square one. This is entirely possible, and logical.
However, this would be the case in a perfect economy where everybody is employed and everybody is paid at a reasonable rate. Then the relatively simple logic outlined in the opening post takes effect. But if there is a sound case to make that the workforce is being exploited, then that logic falters somewhat.
This, for instance, would involve a case where the power lies in the hands of the employers, for example, if there are more qualified candidates available than needed. The employer can then, in a completely open, capitalist economy, offer far lower wages then are fair, and keep the change. This might affect the demand, but would be unlikely to lower it to the extent this margin disappears, because that capital is still in the economy, only concentrated in fewer hands. If this is the case, then the rationale for a fair minimum wage becomes far stronger. Of course, even in this case there will still be some negative effects, such as moderate price rises and a strain on some small businesses, and it would be for those making the judgement, hopefully utilising some economic expertise in the process, to evaluate the pros and cons, and adjudge if the measure would have a net positive effect on the economy. And sometimes it does, and sometimes it doesn’t, depending on the balance of that particular instance.
And in the case where it should be enacted, this is not forced wealth distribution. Forced wealth distribution is extortionate inheritance or property tax, or penalising wealth by taxing at unfair rate. This involves enacting a law that says that an hours work is worth a particular minimum amount, and paying less then that amount is simply extortion. People understand this in the case of monopolies and cartels, so why not in employment law?
Of course, this measure would only be just if the workforce is being exploited. If it is simply a crude wealth distribution measure, and not necessary to protect employees, then it is entirely unjustified. A similar argument can be made with regard to unions.
This may be far more long winded and less dramatic than most of what has been said, but it at least acknowledges that these issues are not as cut and dried as the OP and some others appear to think.