You can get COBRA so it's not that you won't have insurance but rather that you will pay for it yourself. And have 18 months to find a longer term option if you can. It's what I did although I am single without kids so my rate was significantly lower.
Of course that is exactly what your employer paid on your behalf before. So you're basically complaining that other people will now no longer be subsidizing your medical costs. A private system won't help you much. A public one will but merely because people who pay taxes will now be subsidizing you.
This is exactly why a public system would help. Because the amount you pay for healthcare is scaled to your ability (via progressive taxes). Buying a private plan is not.
To see why this matters, imagine embarking on your "conquer the world" startup. You've saved up enough money for 12 months of runway. In a public system you are making 0 dollars and thus won't be taxed. However you will still have full health care. In a private system you will need to pair a fairly substantial amount (but probably not too much more than the amount of taxes that would go to healthcare in a public system) to receive coverage. You now have the following consquences: a) less runway or, b) more time saving up to get an equivalent amount of runway or, c) not having coverage and praying nothing goes wrong d) you just don't pursue your idea because it would be too hard.
Then, in a public system, when your startup succeeds and you make 10 million, you are taxed progressively on that money so as to fund the next hungry young graduate with a dream and a compiler.
I think it is pretty clear that the public system allows for more risk-taking. It is also important to note from your own example that private insurance is pretty expensive unless you are young, single, and without kids. This eliminates a huge swath of the population, all of whom might have different and awesome ideas. We bemoan the lack of gender and racial diversity in the computer field, but I think that the lack of age, lifestyle diversity in start-ups is just as important an issue.
Although one big problem with COBRA is that if you go work for a start up and it fails you're ineligible, there's no one left for you to buy insurance from. That happened to me a few years ago and if the timing had been slightly different it would have left us uninsured during the birth of my son. Another point is that the difference between your employer "subsidising" your health coverage and you paying for it yourself is that under the current system you get a tax break for your employer paying for your insurance that you don't get if you pay it yourself. So not only do companies pay less in general for insurance, the tax benefits represent a huge jump in out of pocket expenses for people looking to leave their employer and strike it out on their own.
Of course that is exactly what your employer paid on your behalf before. So you're basically complaining that other people will now no longer be subsidizing your medical costs. A private system won't help you much. A public one will but merely because people who pay taxes will now be subsidizing you.