There are several reasons why a person might not want to apply for appointment as Queen's Counsel. The most obvious one is that an applicant can never be sure that their application will be successful. A savvy and skillful lawyer might prefer not to participate in the system, rather than submit themselves for evaluation and perhaps, suffer a loss of face when their application is refused. The application itself requires significant effort and consultation with other lawyers who support it, and would not be undertaken by someone who was not highly motivated to achieve the appointment and confident of a reasonable chance of success.
Another reason is that Queen's Counsel are normally briefed to appear on unusually important and complex cases, often with the assistance of junior counsel, by clients who are willing and able to pay the high fees which Queen's Counsel are expected and able to charge. Thus, appointment as Queen's Counsel will change the nature of a barrister's practice. Even if Queen's Counsel agree to work at discounted rates in some cases, they will be expected to refuse, and will not be offered, briefs that are appropriate for junior counsel. An experienced lawyer might prefer to continue their successful practice as a solicitor or junior barrister, rather than seeking recognition as a leader of the profession, who would be expected to spend more time supervising complex litigation and delegating work to junior counsel.
A final reason is that a lawyer may have political objections to the practice of appointing eminent lawyers as Queen's Counsel. They may have republican sentiments and support the office of Senior Counsel which exists in other Commonwealth jurisdictions. Or, they may object to the role of the State in bestowing an honorific title, which is a public privilege that can be exploited for private financial benefit, on an elite group of lawyers who already enjoy significant social privileges.