This is a question that has puzzled me in my research of the history of the Roman Empire.
During the Roman Republic the Patrician class was obviously of paramount importance, & history of the Republic is often taught in terms of the Plebeian class wresting political power from the Patricians. However, following the establishment of the Empire, being a member of the Patrician class was less important than being somehow aligned with the imperial family -- be it the Julio-Claudians, the Flavians, or Antonines.
Augustus had reordered the Roman establishment so that he had some form of control over every possible threat to his rule: over the Senate, the priestly colleges, & especially the military. Moreover, the Patrician class had dwindled in numbers by that point to being as few as 16 in the first century BC (if I remember correctly), & most of them had become relatively impoverished & no longer had members in the Senate. For example, Augustus subsidized the Quinctilii, a Patrician family that had lost its relative wealth over the generations; this was the family the general Varus, who lost the Battle of the Teutoburg Forest, belonged to. Almost all of the major priesthoods were staffed mostly, if not entirely, of Plebeian families; not much later, these priesthoods drew from non-Italians to fill out their ranks. Being a Patrician had come to be of marginal importance.
Yet not only Augustus, but later emperors such as Claudius, Vespasian & others, made an effort to replenish the numbers of the Patrician class. For example, the Acilii Glabriones who were Plebeian in the 2nd century BC, had been adlected/elevated into the Patrician class by Marcus Aurelius' time.
So, what practical purpose did the patrician class have in the Empire? Or were the Emperors simply trying to preserve some relic of the Republic for antiquarian reasons?