With respect to the duties of lawyers to represent clients, I’m afraid I disagree with some of your analysis, David. (Bear in mind, I’m not an American lawyer, so there may be some jurisdictional differences.)
First, with respect to the duty of a lawyer to take a case: a particular lawyer is not obliged to represent any and all clients. Some lawyers are hired full-time by a corporation, a union, a government, or some other organization. They obviously cannot be compelled to represent anyone else, as it would require them to breach their contractual obligations to their employers.
Even those in private practice cannot be compelled to represent someone. For example, if the lawyer does not believe the person has a case, or is lying, or wants the lawyer to do something contrary to the law or legal ethics in litigating the matter, the lawyer should not accept the case.
Another reason may be a conflict of interest, whether personal or professional, which would bar the lawyer from taking the case.
As well, the lawyer can only take a case if he/she is able to defend the client fully. Some lawyers presented with a particular case may conclude that they don’t have the skill set necessary to carry it forward. In those cases, the best legal advice they can give is to help the person find a lawyer who can handle it.
There are also the personal beliefs of the lawyer. If a lawyer truly believes that his/her personal beliefs would prevent him/her from presenting the client’s case, then the lawyer should not handle it. Note that this isn’t a question of disagreeing with the potential client’s views, per se. Rather, the issue is whether the lawyer’s own views would prevent him/her from doing a proper job of the client’s case.
For example, a friend of mine is a very good criminal defence lawyer, but he won’t take cases involving sexual assaults on children. That’s because he has three small children himself, and he believes that his personal reaction to the allegations would prevent him from doing a proper job defending the client.
The second issue mentioned was court-appointments. Yes, the court can appoint a lawyer, but in my experience it only appoints from a panel of lawyers who have expressed their willingness to take court appointments. (In the historical antecedents of the English common law, any barrister present in court could be called on to represent an accused, but the custom developed that if a barrister took off his wig it was a signal to the court that he was not willing to take a court appointment. Or he could just leave the court room when it became clear a court brief was coming up.)
However, all those bits and pieces aside, there is an important principle at stake. That is the absolute duty of the bench and bar, collectively, to ensure that anyone facing serious charges, and who wants a lawyer, is represented by counsel. This was a common law right, and is now a constitutional right in Canada and the U.S. (Canadian Charter, s. 11(d); U.S. Constitution, Amendment VI).
Normally that duty is fulfilled by the private bar and legal aid plans, but occasionally, for whatever reason, a case crops up where a person has trouble getting a lawyer. In these cases, the Crown, the private bar, and the court may have to work together to find someone to take on the case. For example, in the Bernardo case in Ontario, involving a notorious case of sexual abuse and murder, the accused had trouble finding a lawyer after his first lawyer quit. The news reports indicate that the local bar persuaded a very prominent defence lawyer to take on the case, because of the basic principle that an accused person has the right to representation by counsel. After the lawyer agreed to take the case, the court appointed him.