Not really. The primary job of the judiciary, SCOTUS included, is to resolve "cases and controversies." This goes to the heart of judicial restraint, as proscribed in the Constitution, and is commonly referenced in the Court's opinions.
Functionally, SCOTUS ends up writing precedent. But the precedent must flow from the case. Cases mustn't be decided for the purpose of creating precedent.
You don't have to take my word for it. The Supreme Court gets about 7000 petitions per year and only listens to 100-120 of them. Per https://www.ushistory.org/gov/9c.asp the criteria that they choose by is:
Generally, the Court considers only cases that have far-reaching implications beyond the two parties involved in the dispute. For example, a case in which a student sues an assistant principal for searching a locker may shape the privacy rights of all students in public schools. The court also tends to hear cases in which two lower courts have reached conflicting decisions. And it tends to look closely at lower court decisions that contradict earlier Supreme Court decisions.
In other words it chooses cases based on the importance of the precedent that is likely to be set or reinforced. The importance of the case to the people involved is less important than that.