OK.

So they come to E.R., where service cannot be denied.

So either deny E.R. service to those without proof of medical insurance (which is a problem for those who have insurance but don't have their insurance cards), or making it easier for aliens to be authorized to receive services.

If one is in favor of free trade, then one should be against most immigration laws which exist primarily to protect legal residents from competing for jobs, such as tarriffs exist to protect domestic manufacturers and growers from competing for sales.

If an alien has no criminal record, and has a plan for supporting himself, then why should anyone care if he gets a job, pays taxes, obtains health insurance, buys a car, leases an apartment etc? If any alien without a criminal record is permitted to reside and work in the USA, then what will happen is that 99.9% of aliens will use legitimate points of entry. My guess is that the vast majority of illegal aliens are law abiding except for being illegal immigrants and not paying taxes out of fear of being discovered. For those who would not qualify for a residence/work permit, they might continue to try to enter illegally, but if the penalties for using illegal points of entry were raised (and of course, if the border were more clearly marked to prevent accidental border crossing), such activity would be sharply reduced.

Anyway ..

• The ID checks at airports, and eventually train and bus stations exist solely to protect the revenue of the passenger transportation industry. They have nothing to do with controlling borders.
• The liquid checks at airports exist solely to protect the revenue of the airport concession industry. They have nothing to do with preventing explosives on planes.
• The pocket knife checks at airports exist solely to justify an expensive FAM program (i.e. if pax on board can't respond to a hijacker with their own pocket knives in hand, then obviously we need a FAM to protect us). They have nothing to do with preventing hijackings.
• The X-ray your wallet, jewelry, laptop, etc. checks at airports exist solely to allow some TSOs to steal from you (otherwise the TSA would have a professional system like that used in FRA where when pax goes through the WTMD his stuff, and only his stuff goes through the X-Ray, and only the pax and no other pax has access to his stuff. That way if something is stolen, everyone knows it was the screener). They have nothing to do with preventing explosives on planes.
• The mandated TSA locks on checked luggage exist solely to allow some TSOs to steal from you. They have nothing to do preventing explosives on planes.
• The imaging of your naked body at airports exists solely to make ex-government employees who now sell WBIs wealthy. They have nothing to do with preventing explosives on planes.

It is always about money: that is finding ways to part you from your money.