taking the jobs that other people are not willing to work for low wages

I'm good with the points you are making with the exception of this one. Low wage jobs can have low wages because there are people willing to work them. If their are not people willing to work them, then either the job goes offshore (not feasible for most of the remaining low wage jobs) or wages increase to the point were someone is willing to work it.

The strongest arguments for limiting any type of migration centers around stability of the employment markets.