There are a few answers to this question!

First—to be fair, before 1831, the head of the Greek state was a Greek politician—Ioannis Kapodistrias. And he was assassinated because he couldn't disentangle himself from the feuds that ran through elite Greek society, so that might explain why the protecting powers were anxious to get a European prince on the throne. This would be a satisfactory explanation, except for the fact that the powers had tried to put a European on the Greek throne already in 1830, when they approached the future Leopold I of Belgium, who politely turned the offer down. So while having someone not embroiled in the tensions of Greek society may have been a factor in Otto's selection, we can't point to Kapodistrias's assassination as a particular trigger.

Second, and more importantly—having a European prince on the throne allowed for easy entry into European politics. Otto was already connected by blood to the Bavarian throne, and could draw on his father's financial and diplomatic resources. The London Protocol of 1832 (JSTOR link) states as much: "the courts of Great Britain, France, and Russia... being desirous of giving to [Greece] a fresh proof of their their friendly disposition by the election of a prince descended from a royal house, the friendship and alliance of which cannot fail to be of essential service to Greece..." In other words, a European prince, especially one of royal blood (and here we see an element of prestige come into play, as well—no Greek generals or politicians could claim to be of royal blood), was seen as a means of kick-starting Greece's nationhood.

It's worth noting in this respect that most of the Balkan states that broke away from the Ottoman Empire over the course of the nineteenth century also took European princes as monarchs, though in many cases these were selected by assemblies rather than provided by the protecting powers. Thus Carol I of Romania was descended from the German princely house of Hohenzollern-Sigmaringen and Ferdinand I of Bulgaria from that of Saxe-Coburg and Gotha. (German princes were popular choices for new royal families in the early 19th century because they weren't descended from the British, Russian, or French royal families; and later in the century, because they were equally closely related to the former two, as well as half of Europe.)

Finally—having a European prince selected by the protecting powers tied Greece more tightly to those same powers. Some Greeks had sought a European monarch as early as the mid-1820s, floating ideas like Leopold of Saxe-Coburg and Gotha (who would later be offered the crown in 1830 and turn it down) and the Duke of Sussex (a son of George III). These early attempts were more to turn Greece into a protectorate than to make it an independent nation with a European prince, but we can see some continuity from there to 1832. The Greece of 1832 was certainly more independent than the potential monarchy of the 1820s, but still relied in no small part on the goodwill of the protecting powers. The selection of a foreign prince symbolized the new ties connecting Greece to Europe.

SOURCES:

Richard Clogg, A Concise History of Greece, 3rd ed. (2013)

William St. Clair, That Greece Might Still Be Free: The Philhellenes and the War of Independence

text of the London Convention of 1832 (JSTOR link above)