Exactly so. And those slums still persist a hundred years later and in many places they are now expanding out into the suburbs. Ask the people of Long Island. In the mid-1960s we started a war against poverty and as far as i know it is still ongoing and I am still paying massive taxes to pay for it. I can't for the life of me think why anyone would think it was a good idea to import more poverty.
The point is that the vast majority of those people then constitute the mainstream of America today. I think you will find that there has been a complete sea change in the make up of those areas.
You will always have slums..
Immigrants have always started at the bottom and worked their way up. Latin immigrants will be no different.