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.
I understand basic economics so of course see your argument; I'm just telling you what I saw on here. IMO it depends on how far the limits are set by the government. If minimum wage was set at say:£50 ($90)plus social security etc, then I have little doubt that the underground activity that you describe would occur. Of course, it wouldn't get to that as such a rate would cause a national outcry and crisis if the government persisted.
IMO the current rate should not be forcing employers to employ illegal immigrants; as far as I'm concerned if I couldn't obtain an acceptable rate of return if I paid the current minimum wage, I shouldn't be in business!