Your response is tangential to the original point.
OP asserts correctly that increasing supply of labor depresses wages, by lowering the negotiating leverage. Your response handwaves it away with "skilled immigration is better for the whole economy".
Sorry to burst your bubble - this is a thread about balancing the wages / profits split. OP is right; the higher the supply of labor, the lower the price of labor, thus leaving higher proportion of the surplus as profits. Aka the dreaded inequality.
It's fine to prefer profit over wages, if that's how you make your living. But let's not pretend we're for increasing wages while in fact for increasing profit.