On the one hand, it's true that unlike coal mining, most people who work for the insurance industry could probably transfer their skills to other jobs ... but you're still taking away their current job. Even if you include funding for "retraining" into account, you're still telling these people, flat out, that what they do has become obsolete.
But Wait There's More
Perhaps the government would hire them to help manage the brand-new Single Payer system? Well, not all of them ... after all, one of the major advantages of Single Payer is that it's a lot more efficient than the current system. That means economy of scale, less duplication of effort ... otherwise known as firing the shit out of a ton of people who are no longer needed.
Let's say half of them end up working for the government. That still leaves the other half. Even if every single employee were somehow guaranteed a new job, what about having to uproot their lives, perhaps having to move to a different state and so on?
Now, I know what you're saying, "Cry me a river! Different industries are changing and becoming obsolete all the time! You don't see anyone shoring up the abacus or slide rule industry these days, do you?"
True, and I'm not saying making such a sweeping change shouldn't be done ... I'm simply pointing out some of the reasons why it's extremely difficult to do so. This isn't a game of Risk, where you can shuffle your armies around from one place to another like that *insert finger-snapping sound*. These are real people's lives.
Think of it this way: What do you do for a living (or hope to do some day)? Whatever it is, suppose that you were told that the entire field is being eliminated ... on purpose? Even if the reasons for it were sound and society would be better off as a whole because of the change, how many of you would respond by saying, "Oh, well if you put it that way, I guess I'll have to rip up my resume!"
Remember, changing healthcare policy isn't only about what looks logical on paper, it's about persuading people (either voters, politicians, or both) to agree with you. The emotional aspect is a tough nut to crack, especially when it changes from the hypothetical to the here and now.
Speaking of hot-button, high-emotion issues ...
Wait Until The Religious Battles Begin To Rage
You may have heard of a nasty little piece of federal legislation from 1976 called the Hyde Amendment. The short version is that the Hyde Amendment makes it illegal for any federal funding to be used to pay for abortion, except for cases of rape/incest/life of the mother. Medicare is paid for with federal dollars, so no abortions for grandma! Of course, that's not generally a problem for women over 65 anyway (although it turns out there have been a couple of cases of women in their sixties managing to pull off giving birth).