Structural differences between agencies result in different levels of independence. Seven structural features are traditionally associated with agency independence: removal protection, specified tenure, multimember structure, partisan balance requirements, litigation authority, budget and congressional communication authority, and adjudication authority. Some of these features contribute more to independence than others. For example, agencies headed by a group generally have greater independence from the president than agencies headed by a single person, in part because it may take a long time for the president to appoint a majority of a group. (full paper)As they say, these structural features place agencies on a spectrum. They properly reject American law's "false dichotomy" between independent and executive agencies, a distinction which turns on the scope of the President's power to remove the head of the agency from office. This distinction fails to capture the variability of independence and, indeed, distracts attention from the important structural features Revesz and Datla identify.
When it comes to adjudicative tribunals -- bodies established to determine whether individuals are eligible for certain rights and entitlements -- rigorous standards of removal protection and specified tenure are appropriate.
Rejecting the suggestion that the federal government could unilaterally impose term limits on members of the Canadian Senate, the Supreme Court of Canada recently commented expansively in Reference re Senate Reform, 2014 SCC 32 about the importance of security of tenure:
 As discussed above, the Senate’s fundamental nature and role is that of a complementary legislative body of sober second thought. The current duration of senatorial terms is directly linked to this conception of the Senate. Senators are appointed roughly for the duration of their active professional lives. This security of tenure is intended to allow Senators to function with independence in conducting legislative review...A significant change to senatorial tenure would thus affect the Senate’s fundamental nature and role...
Of course, this must be true a fortiori of administrative decision-makers appointed to renewable fixed terms, always looking over their shoulders to ensure that their master is not displeased. While the Senate's independence of mind is vital to the democratic process, administrative decision-makers' independence of mind is vital to the vindication of individual rights accorded by legislation. What is good for all Canadians, in the context of the Senate, is surely good for them in the context of adjudicative tribunals as well. The imposition of fixed senatorial terms is a significant change to senatorial tenure. We are not persuaded by the argument that the fixed terms contemplated in the Reference are a minor change because they are equivalent in duration to the average term historically served by Senators...Fixed terms provide a weaker security of tenure. They imply a finite time in office and necessarily offer a lesser degree of protection from the potential consequences of freely speaking one’s mind on the legislative proposals of the House of Commons.