It is very easy to read Marlowe's Doctor Faustus as a critique of arbitrary power to a significant extent. It is, however, not so easy to suggest that Marlowe intended his Faustus to be read and understood this way. In Marlowe's historical period, two things strongly argue against this reading.
The first is that the Christian religion had a ubiquitous presence and influence in Renaissance life, something akin to the presence and influence education has today: it is an all-pervading fact of life; it is the hope of a better life; it is the rock upon which all aspirations rest. Like education, religion was very difficult to get away from, and it was even more difficult to thwart its controlling influence over all aspects of life. Since life was ingrained with the powerful influence of religion, it is rare at this period that religion--one of two all-pervasive powers--might be lashed out at as an arbitrary power even though the Church at Rome had been powerfully and successfully challenged by the Protestant Reformation: the influence of Christian religion was still ubiquitous.
Arbitrary power is power that is not determined or confined by any law or regulation; it is determined by individual whim or will or desire alone; thus it is not predictable nor is it consistent. Religion at this era was governed, regulated, predictable, and consistent, even if not perfectly so and even badly so. Because of the ubiquitous nature of religion, the milieu wasn't one that readily yielded treatises or diatribes against the arbitrary power of religion.
The second thing is that Queen Elizabeth I was monarch of England. She was during her own lifetime counted as one of England's greatest monarchs. She was successful at bringing her people greater peace and prosperity than had been before. She was beloved as having courage and steely determination to rival a king's. It is also suggested by some historical records that Marlowe was in Her Majesty's employ as a secret agent and perhaps a spy. [There is also a theory that Marlowe's apparent early death was a staged act of espionage ordered by Elizabeth I to protect him from harm.] In light of these facts and half-facts [and speculations], it is highly unlikely that Marlowe would intentionally speak out against arbitrary power with the Queen in mind or with the danger of application being made to the Queen.
Therefore a reading of Doctor Faustus as a critique of arbitrary power would only reasonably be developed from a modern viewpoint without attributing intent to Marlowe. In such a reading, Faustus would be a symbol and metaphor for arbitrary power and the metaphoric outcome of arbitrary power as demonstrated by Faustus's arbitrary, ungoverned and unregulated striving after unlimited power.
All things that move between the quiet poles
Shall be at my command: ...
... can they raise the wind, or rend the clouds;
But his dominion that exceeds in this,
Stretcheth as far as doth the mind of man;
A sound magician is a mighty god:
Here, Faustus, tire thy brains to gain a deity.