There is no problem that can't be solved, not even the sticky problem of how to deal with and manage immigration in the United States. So, I'd like to suggest my perspective on it and a possible solution, that perhaps could be tried also in the large scale that this encompass.
Most visas are based on a sponsor, signing for the petitioned to either study (most often with his/her own money but sometimes also by paid guest attendance and residencies) at a university or college, to be married, thus making the spouse into the sponsor (including assuming financial responsibility to not create a public burden) or to work making the employer into the sponsor (usually within one's field of profession with skills that are sought after and needed, that the majority of the American workforce don't have.). But, if you can't study, you become divorced, or you lose your job, you lose your visa and thus everything you built up to make a home, children, business and social life. While some try to argue a good standing in the community or having been a battered spouse, they rarely win their cases anyway. All this points to the same problem, that I've also encountered several times simply talking to people while I lived in the United States: You're welcome to come and work for me or live here with me, but I don't want to be your sponsor and sign anything. This basically opens the door for both false marriages and buying fraudulent social security numbers needed to receive a salary. Or having to succumb to arguing for a refugee status, which still is to live and work in the United States.
What if, these requirements became removed, just like one can remove one's conditions on a green card after 5 years of consecutive stay? What if, one simply could apply for the intent to either study, work or start a business without any signed sponsor? After all, most good relationships take some time to develop, and best when on equal terms. How would you get a job without going on an interview first? This would constitute indeed the intent to work, that now would be stopped by the border. An opponent might be quick and say that there are entrepreneur visas. Yes, but! An entrepreneur visa doesn't only require a certain sum to be brought into the country, but doesn't constitute an immigrant resident status, which is necessary to be allowed protection under the laws of the United States on equal terms with citizens. You can't really be obligated to follow the laws, if they aren't followed on your behalf (which is why trafficking increases for example) too.
So, one visa with three intentions. Perhaps with the same standard probation time of 2 years and that's it. Individual assessment regardless of how many long lost relatives you can come up with.
When it comes to deporting people, nobody should have to be incarcerated as if they had committed an aggravated felony, according to the Patriot Act, without actually committed one, less been judged for one. Some immigrants become detained alongside American criminals, without even committing any crime.
When someone is found with an expired visa, or not following through on stated intention within two years, that person should be served with a request to leave within a certain time, when appeals are finalised, and only then, become deported simply directly from one's home. Why would the US have any right to an immigrant's belongings as lawfully acquired, besides two suitcases? This is how it is in a practical sense, when one has become detained. A slip and a planeticket. No handcuffs. No prison.