You mention illegal immigration, this is why illegal immigration is bad. It's essentially a flood of people that cannot be supported by the system. Floods are never good, the goal in population transfer should almost always be gradual movements.
If you raise the minimum wage high enough so that it provides for a liveable wage in a major city and are able to enforce it, then the amount of people willing to pay migrants for work will collapse and the migrants will stop coming to the city.
So you either accept the conditions and wages the migrants are being paid, or you eliminate the very reason migrants travel to cities in the first place.
I want everyone to live in comfort, but it's much more complicated than "just open all the borders and raise minimum wage".
Anecdotally, tens of thousands of people have been moving to my city every year for over a decade. The rents have increased dramatically, forcing many out of their homes. Traffic is horrible. A few years ago, a severe drought led to serious water disputes between the city and nearby farmers. We're doing much better now, but another drought will come, eventually, and with all of the extra people, it will surely be worse. At the end of the day, there are only so many folks that an area can support at all, let alone comfortably.
That’s why the Bay Area operates through proxies like building permits and rent control - explicit immigration restrictions are a violation of citizens’ rights and would be easily smacked down in court.
It doesn’t matter how convenient it would be to control migration - if you want to do that, you need to secede. The American community has rights that supersede your neighborhood’s.
> If you raise the minimum wage high enough so that it provides for a liveable wage in a major city and are able to enforce it, then the amount of people willing to pay migrants for work will collapse and the migrants will stop coming to the city.
While I understand the theory, the reality in places that raise minimum wage is much more complex.
I agree free movement of sapients should match the ease with which capital moves. However, atoms and bits have different energy profiles, and hence different logistical tails. The logistical tail to support the marginal person moving into full citizenship benefits and rights of say, the Democratic Republic of Congo, versus say, Singapore, are vastly different. How would you propose to bridge this logistics gulf, which doesn't even address the cognitive and knowledge gulf of citizens from more impoverished nations moving into more prosperous nations with a higher societal- and culturally-expected baseline of cognitive abilities, skills, and knowledge? This has historically been a tough problem to crack at the developed nation side to achieve unrestricted immigration, hence why I suspect there is increasing emphasis upon improving the situation at the developing nation angle (a "rising tide" strategy).