That can be seen as just part of the burden of charging you with a crime: the state needs to provide you with a judge, jury, and counsel.
Amd it's not the greatest example of rights-in-action if you ask me. Often such counsel is overloaded and just tries to negotiate a plea deal rather than provide a robust defense.
The solution to that is acting positively to create a system that we think is strong enough to withstand challenges in the courts.
You don't have to wait until the courts strike down your public-defender system for being wholly inadequate, for example, you can properly fund the system in the first place and then the courts won't be legislating it.
"standard of care" is the term that comes to mind. And yes, like all human systems there will be disagreements about what that standard should be, and some system for resolving those, and in a handful of cases people will receive unfavorable outcomes. The point is to act to minimize those outcomes and provide high-quality care to as many people as possible.
The alternative is having those arguments with your insurance company, and you will lose. The death panels exist, they always have, and they are held in a building with "Aetna" on the side.
If "acting positively" means "work it out in the legislature", then we agree. But the language of rights starts to push this responsibility into the courts (at least in the US).
I am not saying there will be no arguments. I'm just saying we shouldn't hammer out the details of a medical system in the courts.
If you are trying to convince people to have the government gatekeep their healthcare, then I don't thinkt he attorney's provided by the "right to an attorney" are something you should mention.