It can vary heavily like you’re saying. By law, all hospitals must treat all patients who arrive at the ER.
Most hospitals have programs so they can provide care for those who can’t afford it, though. Usually around 20-25% of their revenue is used to cover those patients.
If you qualify for Medicaid, they can backdate your enrollment so you’d be covered even before you arrived at the hospital. Coverage can vary, but this usually should cover all medical bills at no cost.
The big issue usually isn’t people who have no insurance or are too poor. It’s from hospitals treating you while your insurance refuses to pay. Normally this is because the bill was miscoded, but it can also be due to an uncovered treatment, high deductibles and OOP limits, or the insurance just being greedy.
Sometimes the hospital or doctors can work things out to minimize your bills, other times they can’t.
A lot of the protections above came about because of the Affordable Care Act (Obamacare). Before then, there were common horror stories of people who had hundreds of thousands in medical debt because they reached their lifetime maximum coverage - something that’s illegal now. Insurance could (and often would) just tell people they’re on their own from now on because it’s too expensive to keep them alive. Your coverage could be changed whenever the insurance company felt like it. And up until last year, they could make you pay for treatment if an out-of-network doctor decided to pop on by while you’re at an in-network facility.