Something I didn't see mentioned in the other answers is that the use of "I" you described is partially English-specific, in that there are languages in which the word for "I" can often be omitted due to inflected verb forms. Thus, in some languages, the repetition of first-person singular verbs can be less conspicuous because you don't end up with the same word beginning every sentence.
Mainly for this reason, I'm pretty indifferent about this particular style issue; that is, it generally doesn't bother me, and I'm not led to believe that the writer is egocentric, unless there are other signs of this personality trait.
The way we experience life is subjective, so there is a natural tendency to say things like "I had no idea that..." because we wish to share experiences.
Some general thoughts that may or may not be useful to you -- I find these style guidelines to be the most important, in no particular order: (1) Write in a way that is appropriate for your intended audience. (2) Write in a way that you find interesting.
Reasoning: (1) Reaching a target audience indicates good communication skills. (2) Having a well developed sense of personal standards indicates substance/character/ownership.