Hi I think you have been misinformed, Charlemagne was not illiterate for his whole life. He eventually learned to speak as well write in Latin and some Greek in addition to his native Frankish.

As for your question about how common it was for illiterate people to be in power during this time. Quite frankly yes it was, Since the fall of the western roman empire, much of what we now call europe broke up into much smaller territories as such the need for large administrative bodies who could read and write diminished.

We saw a increase in literacy when countries started to get larger both phiscaly and fincially. This was done out of nisesity as it is harder to negotiate a peace treaty if you can not read what the treaty says.

for more information on the effects of economic growth and growth of literacy in europe. see http://web.stanford.edu/~moore/Chapter6.pdf

Charlemagne could read and speak Latin fluently and understood Greek (although he wasn't conversational). Where did you come across this?

In Charlemagne's Frankish Kingdom, there were language barriers among his royal representatives throughout the kingdom that presented a need for him to speak and write several languages. In Aachen, his native tongue of Theodisk, or Deutsch, served as the common language used among his court subjects. His representatives across the kingdom, however, spoke a crude form of Latin, which Charlemagne spoke and helped make the diplomatic language of his kingdom. Worried about the dying out of his native German dialect, he preserved it in songs, calendars, and personally wrote a basic grammar.

Source: "A Mighty Fortress: A New History of the German People" By Steven Ozment

So Charlemagne was not at all illiterate, and neither were many of his representatives and court members, due to necessity in maintaining his kingdom. Where did you come across someone stating his illiteracy?