It seems to me we need to resurrect the effective idea of sponsors and bonds. If someone wants to immigrate to the United States, they should be required to have an American citizen sponsor them. The sponsor should be reputable and be able to post a substantial bond for the invited guest. A citizen would only be allowed to sponsor a single person at a time. After a period of years, the bond would be returned.
This shifts the burden of screening to individual citizens and also encourages reputable people to be allowed in.
We need to end the practice of babies being born in the US to be natural citizens. This is dangerous. Only babies born to citizen parents can be American.