Uhhh... no.
Stopping “chain migration”, the practice of bringing in extended family of recent legal immigrants simply because they are related in some manner to the principal immigrant, who may have been chosen by lottery and for no other reason or merit, drew a winning ticket, is but the FIRST step in ending a wholly irrational system of admitting applicants for citizenship.
Entering the US, then immediately applying for government assistance, is NOT a way to achieve the “American Dream”. If the immigrant is not immediately capable of either being fully self-supporting, or have the sponsorship of someone who is willing and able to provide the remaining needs for support, without resort to government assistance at any level, is cause for deportation.
This implies a good degree of fluency in the English language as spoken in the US, and some kind of valuable skill sets that is of economic benefit to the continued prosperity of the nation and the locality in which the individual settles.
The second part of the reformation is to eliminate the quotas by country, in which there is a lottery to chose who may emigrate to the US, without regard to any application of standards and tests to determine if the person chosen is morally, temperamentally and educationally fit to assimilate as a US citizen. The net is cast far and wide, to offer a place to those all across the world, who are willing to assume the obligations of becoming a US citizen in every sense of the world, no dual citizenship permitted after attaining the age of twenty-one years of age.
And of course, nobody is admitted except through the legally established routes and entry points. Merely jumping the border or swimming ashore is not, in and of itself, any kind of legal entry. Just build the wall and enforce current law.
There is, of course, the problem of refugees, those who are fleeing a very real persecution elsewhere. In that instance, these refugees shall be held at an offshore point or closely guarded detention facility without the extension of rights afforded to legal residents or citizens, until their circumstances may be sorted out. If the “persecution” they claim to be fleeing turns out to be falsely described, and they are in fact real criminals by any standard in their place of origin, they are returned to the authorities of that locality. If they were criminals there, they would likely also be criminals here, and that, we do not need. Those who are truly in need, thorough economic pressures or by very real harsh oppression, may petition for and be assigned to a responsible party or agency here in the US, to help them assimilate and start a new life, under continuing and responsible scrutiny until they are established, which means no government financial support or granting of any rights beyond that of a legal resident non-citizen.
Visa overstays must be more carefully controlled, by requiring a re-registering as an alien non-citizen resident at fairly frequent intervals, say every six months. Failure to maintain the registration is cause for immediate deportation to country of origin, and any hearing shall be IMMEDIATE, no release back into the community.
“Anchor babies” born on US soil not as part of a diplomatic corps or exchange programs, may be granted the OPPORTUNITY to apply for US citizenship upon attaining the age of twenty-one, but all the other requirements must be met (fluency in English and verifiable knowledge of the responsibilities of US citizenship, through taking a comprehensive test), and swearing an oath of allegiance to the United States of America, relinquishing any other national allegiance. Birth certificate alone is not enough.