Many people with money but without insurance do go and get b*tch slapped later by their ~$10k-$200k medical bill. It’s a reason why medical debt is the LEADING cause of bankruptcy in the US.
Many people without money or insurance also go but since they don’t have assets, they just don’t pay and the hospitals can’t collect on them. So the hospitals have to raise costs on people with money to pay for people without money.
The second scenario actually caused a hospital I knew of in Dallas Texas to close down because it had (according to the locals) “too many illegal immigrants taking advantage of free healthcare”. Dallas Texas is somewhat close to the Mexico border.
I personally knew of a vagrant woman with a prior medical issue that bragged about happily racking up the hospital over a million dollars in expenses after staying in a hospital bed for a few months. She didn’t express concern about having to pay for any of it since she doesn’t work. I wasn’t sure how to feel about that.
I once paid $8k while my health insurance paid $43k when I spent just half a day in a hospital bed in Colorado after I fell and broke a bone.