Strong opinion loosely held, but the U.S. immigration (not refugee) policy should be:
1. You are going to school? Great! Go to the DMV with reasonable documentation (student ID and registration paperwork?) and you get a year-long visa. Renew each year, welcome to America!
2. You have a job? Great! Go to the DMV with reasonable documentation (a couple pay stubs?) and you get a year-long visa. Renew each year, welcome to America!
3. You don't have a job yet? Great! Go to the DMV with reasonable documentation of self-sufficiency (bank statement?) and you get a 3-month visa while you look for work. Renew each 3 months for as long as you can prove self-sufficiency, welcome to America!
4. You have none of the above, but you are the spouse/dependent on someone who does? Great! Go to the DMV with them, with proof of the relationship (marriage/birth certificate or the person signing an attestation) and you get a visa to match theirs, welcome to America!
5. You have none of the above but you are a refugee? Not great for you, but: go to the DMV to register yourself and get a date for review. With the money we save on enforcement, that review should be within weeks if not days. Welcome to America! (for now, subject to review)
6. You have none of the above and run out of money? I'm sorry about that, please return to your home country.
7. You're on the national list of Certified Bad People? You're going back to your home country, No America For You. And we have biometric information on you to ensure you never come back. Did I mention the DMV gets FaceID and DNA swabs?
Kitting out the DMV will cost a fraction of what enforcement would cost. Oh, and quotas should be generous but not infinite.
Generally a sensible list, except I'm sure you have seen how the national list of "Certified Bad People" is used these days. A majority of people that ICE rounds up have no convictions or traffic type issues (https://www.cato.org/blog/5-ice-detainees-have-violent-convi...).
Yeah, I'd at least put the bad people list in some way under the control of the judiciary, but in the end you pretty much have to assume good faith when designing any system of supreme control.