All of this
modulo American healthcare means a lot of people who follow this script still end up with nothing. This is especially the case for entry-level jobs and other careers that are more available to the newly arrived.
If you work in a median-income job and are miserly for a long time and save up a year's income, you will have around $60k in the bank. Since you don't have a pension, materially all of this will be in mutual funds or the like if retirement is in your plans. But great, you have savings!
Now let anything happen that requires you to visit a hospital unexpectedly. Let's say your appendix bursts, so you couldn't meaningfully have avoided this calamity.
The average cost for an appendectomy in the US is $33k[1]. That's just the surgery, so assume you'll be out $40k or more. Now let your boss be a miser (like yourself) who decides to fire you because you can't come in. Depending on how quickly you find another job, how much it pays, and your ability to avoid another unexpected disaster (car trouble, sick kid, etc.) you could quite easily burn through the entire $60k of your savings from this one incident. So the very next time this happens, you're no better off than the folks who saved nothing.
But wait, it gets worse! Since your $60k was primarily in retirement savings, you will likely end up paying penalties and taxes for early withdrawal. So you will end up spending thousands of dollars to access your money. The rules are designed to kick you while you're down in this respect. And now you have no retirement savings, so people can talk about what a freeloader you are in your dotage.
(The probabilities get worse as you get older. For an example of how bad, check pricing for long-term care coverage or long-term disability coverage. Basically -- you can't reliably out-grasshopper biology.)
Our healthcare system in general makes the grasshopper approach more about luck than is apparent at first glance.
1 - Obviously, insurance currently will pay a large portion of the $33k, as the ACA mandates that health insurers sell a useful product. But this has not been the case except for the last 7ish years, and may not be the case again in the near future. It would be foolish to expect health insurance to function as "health insurance" in America for any extended period of time.