How? How are ERs even equipped for routine health care?

It's all the same hospital. The ER is just a different entrance. It's just a way to get into the hospital. You wouldn't be treated in the same area as the real emergencies.

I have heard that this means they (the poor) only get health care when things have developed too far.

That's incorrect. They don't turn anyone away. If they did, they'd get sued. I've actually seen lawsuits 1st hand where illegals sued hospitals not for being turned away, but for supposedly not getting adequate care - they always got care. One case in particular an illegal woman was pregnant & went to the ER for some minor bullshit, got some pills, sent home. The hospitals are def overcrowded & do rush you. She had a miscarriage a week later & sued the hospital. Total bullshit case.

Very common. Illegals know they can win the lotto & get free money by suing, so they run to scummy attorney mills that serve their community & sue every chance they get.

So if I'm in the US and need treatment, all I have to do is go to the ER and pretend to be illegal, and I'll get free health care?

You don't have to pretend to be illegal. They're treat you regardless. They'll ask for insurance, but if you say no, they don't turn you away.

Do you have personal experience of something like this

yes I worked for a law firm that did malpractice defense in LA & saw lots of it.

you can also look it up, it's a well known thing. also 100% of poor people in the US are covered by Medicaid & get free health care (not needing to go to the ER) but poors are lazy & don't bother signing up. The hospitals have to keep pressuring them to do the paperwork.