The Biden Administration just like the Trump administration before it does not with the sole exception of Venezuela advocate regime change in foreign policy. Iran should be another exception. Iran is an exceptionally dangerous regime which poses a significant strategic threat against the United States and its vital national security interests.
A no-fly zone is however not a regime change policy per se but in the best case scenario would a no-fly zone over Iran lead to an armed uprising with US air support throughout the entire Iran. In the second best scenario would the armed revolt happen only in the ethnic periphery which comprises about half of the population of the country and most of its oil resources. Shrinking Iran to Persia and establishing a series of KRG-style self-governing regional governments would nevertheless be a significant achievement of a no-fly zone policy. If the regime falls, then so much the better – if not and the country shrinks, the empire has been decimated and furthermore deprived of most of its oil revenues.
A no-fly zone over Iran should definitely be part of the new Plan B to the JCPOA. This is a vital US national security interest indeed.