First, understand what universal health care involves - Britain may have private alternatives to NHS - which results in the same doctor saying to an NHS patient - “I can do that treatment for you in 6 months on NHS< or tomorrow if you pay me twice the NHS rate.” Canada specifically chose to adopt a different standard - a doctor is either completely in or completely out. (The health schemes are provincially run, but the feds provide the guidelines.) If a doctor chooses not to accept the published fee schedule for all covered treatments, then neither he nor his patients get reimbursed. There is not a big enough contingent of pay-as-you-go patients to keep a community of doctors in green fees and gold club dues. There are no plans that offer private insurance to cover what government health care would otherwise cover, and no employers interested in signing. So… the government fee schedule is the only game in town. The government tells doctors what they can charge or they can’t play. Why doesn’t the USA have UHC? Because that concept would likely go over like a lead zeppelin in the land of the free.
the government(s) in Canada run all the hospitals, essentially. They health authorities give them money, assign their budgets, since the patients pay nothing. The same applies to what passes for “insurance”, the administration of health care payments and billing. Apart from the simplification of billing - no arguments of in/out of plan, what’s covered, etc - the system also seriously limits the gravy train compared to the USA. We don’t have presidents of hospital boards getting millions of dollars. The guy who runs the health authority for almost a million people (the first number google found me) got about $C500,000 or about $US400,000. They are a government body, not a profit center. OTOH, frivolous lawsuits and “pay to go away” settlements are a lot fewer. Suing and losing in Canada most often means the loser has to the winner’s legal bills, so malpractice insurance - another big cost in the USA - in less in Canada. Juries are a lot less generous when they are giving away their tax dollars. Hospitals rarely advertise, except the fund-raising foundations to do additional charitable works. All in all, the gravy train is a lot smaller in Canada. That it seems to me is another problem for the USA - with UHC, the number of people whose income will be adversely affected would be large, and they are the ones rich enough to lobby effectively. And, oh yeah, the major buyer of pharmaceuticals in Canada is the government(s) so prices are much lower than in the USA. That’s how the USA spends 16% while other countries spend 8% GDP.
The reason for the individual mandate in the USA was that if you waited until people figured out they needed health care, you only insure the sick ones and the price per patient is too high. The whole idea of forcing people to sign up was to spread the cost. If people could sign up for a form of Medicare then the effect is simple - any policy more expensive (when considering co-pay) or more annoyingly complicated to use, will quickly be dropped by anyone who can sign up with the government instead. Companies would probably happily drop their plans once their employees had a viable alternative. Again, doctors and insurance companies (and hospitals) have a vested interest in keeping patients on more lucrative plans.
To answer your question, you would have to determine whether there would be a trickle or rush of people singing up, and that depends how other plans compare. A lot of employers pay for part or all of their plans, so the cost to the employee may not always be a good measure of how competitive Medicare could be.
Medicare in Canada did not emerge without some friction - there was at one time a doctors’ strike in at least one province to protest being forced to accept government fee schedules, and occasional actions since then. Plus, once people have actual health care, they use it - there are waiting lists for procedures, and in many places, difficulty finding doctors with opening for more patients. Medicare enrollment in the USA may be affected by how the industry reacts to being forced into that box too.