Anyway... This is going to be a long post.
Universal Health Care in and of itself is a fine idea. The devil is in the details.
When you're talking about UK or Canada, The government pays the bills and they set the prices. There are often quite long wait time for less common procedures and for diagnostics or surgeries; there are often much quicker turn arounds for minor illnesses and injuries. It can work well, but it's not without challenge.
In the US there are several different factors involved, and it's not all one thing.
Some people object to UHC for philosophical reasons.
For many people, the tax trade-off is a problem. It might seem trivial to say "oh, but you'll see the benefit of those taxes and it will be better". The problem is that a large amount of health insurance in the US is provided by employers, and those employers frequently pay 90% or more of the aggregate costs - excluding cost shares (deductibles, copays, coinsurance, etc). Many employees will pay less than $100 per month for their health care coverage, because their employer is paying $900+. There's a lot of variation involved, so consider that a very broad average. It varies by the ages of the workforce as well as the part of the country; it cost a lot more for a person in NYC than it does in KC, for example. All of this creates a layer of complication that often gets little thought when we're talking about UHC. Realistically, if UHC goes into place, it's unlikely that employers are going to increase everyone's wages by the same amount they were paying for insurance - there's a very high likelihood that many employers would pocket a good chunk of that as profit, or use it to expand their business, or cover debts, or any number of other expenditures instead of giving it directly back to their employees. The result of this employer dynamic is that for many people, they would see their taxes go up by more than they pay directly for their care, but they would not see their wages go up. For many people, it's likely to result in higher taxes with no additional benefit to them.
One of the other challenges is that the providers in the US are generally for-profit. Not just the doctors, but also the hospitals, the stand alone facilities, the urgent care centers, the labs, the diagnostic facilities, the device manufacturers, and the pharmaceutical companies. Every cog in that process is making money off of people's illnesses and injuries. Insurers have their profitability capped, due to minimum loss ratio requirements from PPACA - we are required to spend at least 80% of our premium revenue on customer health expenses. If we don't spend that much, we give the money back to our customers in the form of a rebate.
Most of the proposals for UHC put forth by congress in the US have been framed as "guaranteed insurance benefits", much more similar to Medicare where the customer still has cost sharing for their coverage. Those proposals haven't included any measures to reduce the cost of delivered care, which means that it's still going to be very expensive. An expansion of Medicare to include a younger population would be a really good start... but that gets push back from the entire medical community because Medicare's fee schedule isn't as high as they would like it to be - it doesn't give them enough profit to keep building new fancy medical centers in highly populated urban areas, regardless of the fact that there isn't a need for more hospitals or infusion centers there, and less populous areas are in health care deserts with no reasonable care available to residents at all.
There are some reasonable possibilities out there. Maryland did a thing a while back that has been working pretty well by all accounts - the state more or less defined the fee schedule for all services and all hospitals in the state, and that's just what providers get. IIRC (and I might not) they use the same schedule for all employer, individual, and Medicaid coverage - I think it doesn't supplant Medicare fee schedules though. Despite all their complaints, hospitals and doctors haven't gone bankrupt and it hasn't caused delays in accessing care.
I generally like the idea of making the delivery of healthcare a public good. Under my preferred approach, all doctors, nurses, hospitals, and other facilities would be owned and operated by the federal government, with professional staff paid a salaried wage. The government could then set a reasonable fee schedule to charge insurers - and potentially even offset the needed taxes through that means. It would allow employers to continue providing health insurance to their employees, since that's one of the ways that companies compete for staff. It would allow the current insurance industry to continue under something much more like Medicare Advantage. I think that would cause the greatest benefit to citizens with the least disruption and job loss. I'm sure there are some wrinkles that need to be ironed out, but that's generally my starting point.