In Norway, there is no dedicated public defender system. Instead what happens is that the bar association negotiates rates with the government, and most lawfirms will take cases paid for by the government.
There are still limitations. E.g. someone going private could hire a team to spend whatever time necessary while someone being defended under the public system will get one lawyer subject to billing limitations. And people relying on the public system does not get to pick and choose. But at least you have a good shot at getting someone good, that is not overloaded with cases.
As an example, I was sued by the government for refusing to accept formalities around my refusal to accept conscription (a small number of people go to jail in Norway for it every now and again for 3 months or so, and they keep making the accepted reasons to get out of it more lenient to make people just pick one of the accepted reasons rather than make a point; for my part it was very much to make a point, though I didn't end up in jail in the end), and my government appointed defence lawyer was one of the top lawyers in the country, who had argued cases in front of the Supreme Court multiple times, and who had conscription related cases as a special interest.
It's quite tragicomic to me that left-wing Norway has privatized the public defender system exactly to provide more equal access, while the US hold on to a socialized system that practically guarantees unequal access to justice.
