Yes, I have. The post office seems to do an EXCELLENT job of delivering mail at an absurdly low price (for standard letters or postcards), although when I lived in Chicago for a few years I found that a certain portion of letters were never delivered.
A number of years ago the DMV (I was in New York and New Jersey at the time) offered terrible customer service; these days the DMV I have gone to (New Jersey and Pennsylvania) seem to do an excellent job.
What I can conclude from this is that quality varies, whether in private industry or public services.
A single-payer system isn't a state healthcare system.
It's a public-private healthcare system in which a single entity pays all healthcare providers for health services rendered.
Individual providers would still be free to negotiate their own rates with the single-payer entity.
Individual providers would still be free to provide concierge medical services or other non-covered medical services (for example, most plastic surgery).
Individual providers would still be free to distinguish themselves on the basis of patient service.
And with all due respect, the problem with the post office is that the GOP requires it to pay for decades of upfront expenses now rather than when those expenses are incurred, unlike a private business, and the GOP won't actually let the post office operate anything like a private business. If the post office could operate like a private company it would shut down every rural post office in America, since those are just money drains that detract from the profitable urban and suburban facilities. If the post office could operate like a government agency again (like it did before Reagan), it would run as smooth as butter.
The ACA has always hovered around 50% favorability and 40% unfavorability nationally, so "extremely unpopular" isn't accurate. Additionally, support among voters for Medicare for all is about 70%.
The Tea Party predates the ACA and was more a general anti-Obama movement than specifically motivated by one policy.
ACA was extremely unpopular because of how it was characterized. It is extremely popular today.
Have I been to the post office or the DMV? Sure. And when there are a ton of people who want to use a service, you tend to have to wait.
Have YOU been to a for-profit emergency room? Or a for-profit, non-fast-food restaurant? Hell, go to a Fed Ex or UPS store. They won't be perfect, and you will wait in line.
There's many good reasons to avoid nationalized healthcare. Have you been to the post office or the DMV?