The belief that minimum wage shouldn't function as minimum wage (despite the very term stating otherwise) has nothing to do with economics and everything to do with the greed of the few and the ignorance of many. Judging by your posts I would guess you are the latter.
Contrary to what you're thinking, simply stating that your argument "sides with economics" doesn't make it so.
To state that the lowest in our society with the least going for them who take on the jobs the rest of us aren't willing to do and have the option of not doing should have their basic needs met is not idealism. It is simply common sense.
What irks me here is that your argument against raising min wage isn't that the people on it are able to sustain themselves fine already.
Instead your argument seems to be that they shouldn't.
And that is not what civilized society is about.