I think what you described are sides of authoritarianism and libertarianism, not right and left. From my observation, both left and right are trying to enforce something with laws, but things they want to enforce are different. These two spectrums are orthogonal imho (i.e. you can have authoritarian right and libertarian left)
I'm a big fan of the political compass model. I think it does a great job of creating enough space to lay out most people's political values. But regarding immigration and law enforcement, at least right now, the right in America tend to be pretty authoritarian while the left tend to be fairly libertarian.
Of course that flips when you jump to the issue of pursing white collar crimes and regulatory violations.
BTW, in this context I'm using 'right' to mean the group of people that largely votes Republican and 'left' to mean the group of people that largely votes Democrat.
I can't see how the left being libertarian on immigration while at the same time voting for large social welfare programs can work. you can have only one: no borders or social welfare. You can't have both at the same time (until globalization will even out income in the whole world)
Perhaps we could go 100% libertarian first (no borders, no taxes) and after a while go 100% social (not sure how globe-wide social welfare can work tho)
I'm not sure. That's a huge issue which I'm woefully under-qualified to have a strong opinion on. I do know that Switzerland has generous social programs for citizens but allows people to live and work there without full citizenship. Which is one partial solution. Though they now have the pretty ridiculous problem of having 3rd generation Swiss immigrants who aren't Swiss citizens.
Problems of immigration and citizenship go all the way back to republican Rome. The answers are crappy and few epspecially with several global humanitarian crises underway.