The Chief Justice's incentives
The Chief Justice of India has many levers of power.1
First, they have a bully pulpit. They can make speeches at universities and bar associations to signal attitudes to judges and lawyers.
Second, they are the master of the roster, which means that they have final control over the constitution of benches of the Supreme Court. They decide which judges get which cases.
Third, they run the Collegium, which makes (theoretically binding) recommendations for the appointment of other judges. This power is heavily qualified, in practice, by the fact that the Executive can delay, and generally defeat the Chief Justice by refusing to make the appointments. The judicial branch, as Hamilton said, has neither sword nor purse, neither force nor will, but merely judgment.
Fourth, they are the CEO of the Supreme Court's processes. They can make technological innovations and improve procedure.
Fifth, they are a judge of the Supreme Court. They can decide cases and write great judgments if they are so inclined.
Tradeoffs, Tradeoffs, Tradeoffs
CJIs have many priorities. Their legacies are defined by:
Their general popularity at the time they leave office;
Their contributions to the development of the law;
Their ability to maintain the independence of the judiciary and keep a patchwork simulation of the rule of law going;
Their administrative efforts, which are primarily directed towards two complementary goals, which are (a) the appointment of judges to fill the many vacancies in India's judiciary and (b) reducing the gargantuan number of pending cases before the Supreme Court and the High Courts.
(3) and (4) are somewhat contradictory. To appoint more judges, the Chief Justice needs the assistance of the executive. And when the Chief Justice writes judgments expanding the rights of citizens and constraining the powers of the state, the Executive is naturally annoyed.
And so the Chief Justice must make compromises. These compromises are not unusual. There are structural contradictions at the heart of the role, and it makes it difficult to be both a popular and an effective Chief Justice.
This Chief Justice is not entirely exceptional by the standard of having additional levers at the time he took office. While this is the first time both a father and a son have run the judicial branch, there are many examples of people related to each other in the Supreme Court. CJI M.H. Kania (1991-92) was the nephew of CJI H.J. Kania, the first Chief Justice of India. The late Justice K.K. Matthew is the father of Justice K.M Joseph, both of the Supreme Court. Chief Justice PN Bhagwati was the son of Justice Bhagwati, a former Supreme Court judge.