"All it REALLY does is increase unemployment because business that have jobs where the productivity is lower than the "living wage" will no longer hire."
For several years we had no minimum wage (I'm assuming that's what is meant by "living wage", correct me if I'm wrong)here in the UK before the current government(labour) was elected. Not sure what it is (about $9-10) but there do not appear to be any negative effects on the economy. Something to do with the fact that people earning minimum wage need to spend all the money they earned. Read it on here by someone hitherto sceptical about minimum wage so for me at least has some credibility.
We're not talking about some radical new theory here....you simply cannot legislate the value of labor without negatively effecting the economy....period. No-one disagrees with that....no one. There is no ongoing debate... it's simply a fact, like gravity.
You seem to be politely describing you personal view, and I can accept that, but to me it sounds like someone trying to explain to Newton that sometimes the apple falls up.
If you fix the price of Apples you change the market for them. If it's too low you get shortages, if it's too high, they rot on the docks. Labor is the same thing. If you "fix the price" at too high a level, the worker will rot on the docks... or "become unemployed."
That's it. There is no reasonable way to say "yes but" to this fact. When you set a minimum value for labor (and call it a living wage or whatever) you will no longer employ people who's productivity does not exceed that value.
There is one other option however, you could be forcing employers to hire illegal immigrants and illegally pay them below the "living wage" level. Illegals don't complain when you pay them half the "living wage" and usually accept it happily. Of course now you've gone and created an entire underground economy which is no longer subject to your laws.
But all in, I'd still call that a negative effect.