Most of the sentences can be trivially rewritten without the use of "I", but the author still chose to use it anyways.

  I have been contacting a large group of people and many
  have specifically asked if you were attending.

Versus..

  Many people on the contact list have specifically asked if
  you are attending.

And likewise, there are sentences the "more powerful" person could have written with the word "I", but did not.

  The idea of a reunion is a nice one

Versus..

  I think the idea of a reunion is a nice one

The last two lines are very telling.

"The idea of..." line suggests that whatever is being said is a known fact, that the reader should take it on authority, where as adding "I think" immediately makes it sound like the writer is less sure of themself and only has an opinion that they don't want to push on anyone.

Ok so to summarize: when they are talking to higher-ups, people don't want to make strong claims so they use wordings that make it explicit that this is "only" their personal opinion rather than an absolute truth. And they typically do so by using the word 'I'. Which is therefore a good indicator to detect who's the higher-up.

I would agree with this, but this all very implicit in the post.

  The reason I'm writing is that I'm helping to put together a conference on [a particular topic].

Really does need the personal pronoun, and the usage in subsequent sentences may just be the author continuing to write in the same "style".

So how about "We're putting together a conference..." or "Org name is putting together a..."? Even if you're the driver behind the conference, it just seems more charitable to use "we".

As kids we were taught by our parents to avoid I, me and my in letters we wrote to our grandparents. It was (is?) seen as rude. The justification wasn't about status at all, but rather about ego. The worst offense was beginning a letter with I. At least it was in German in the '70's. Anyway, the habit stuck but lately I find myself slipping.

I was never taught anything like that, but in one of my high school English classes all of our essays had to be written in the third person, so I get gain some experience doing it.

I actually put it to good use writing some email newsletters for a local conference where I tried to eliminate usage of I/we/etc because I felt that it was more professional.

In Germany in the 90s is was still common place. And I see myself carefully avoiding the first, singular personal pronoun.

Modern USAian usage seems to favour, "I myself". Make of that what you will.

It's standard negotiating practice to attribute all decisions to a larger group one is a part of. People who do this by using passive tense and "we" instead of "I" will tend to have more status over time.

Its standard management practice to use "we" when referring to work done by others.

What about the initial email, just dropping the I? I get email like this a lot in the professional world, and for whatever reason I've found myself sensitive to it:

    Dear Dr. Pennebaker:

    Was part of your Introductory Psychology class last semester. 
    Enjoyed your lectures and learned so much. Received an
    email from you about doing some research with you. 
    Would there be a time to come by and talk about this?

    Pam

It has the minor problem of dropping a significant, not-to-be-assumed part of every sentence.

I see that commonly in three scenarios: 1) irc 2) from people who learn to write English as a second language 3) from people with whom I have a familiar relationship - generally rendering the pronoun unnecessary.

I get it a lot in unsolicited requests and workplace emails. Perhaps as a misguided effort to be more professional. Or a subconscious realization of the topic of the article.

An example of an email I got just today:

    Hi <mr-ron>,

    Saw your company's ad on a taxi yesterday, checked out your product,
    and was wondering who you are using for colocation.

    Regards,

    <person i will not be responding to>

Really odd. It's always seemed to me that "like", "um", and "uh" were often used as filler words to 'distance' yourself from the thing being discussed.

This seems even further in that direction - instead of distancing the author, it removes him entirely from the discussion.

Writing grammatically incorrect emails is probably the lowest status of all.

Hah, totally reads like an email my boss would send.

The article implied to me you'd see the effect between people already well-acquinted, so long as a power gap exists.

I do agree the "self-conscious" explanation seemed like an interpretation without evidence, and struck me as incomplete. I'd guess it has more to do with intentional signalling, and that it's often conscious, even if that consiousness is not of "I"-frequency per se. That is, when writing or speaking as a supplicant, you're aware of using language that sounds "respectful" or "polite," and "I"-frequency is a feature of such language which we internalize.

Which is to say that we often write in this style because we intellectually know it's appropriate, even when we are not affectively feeling any emotion like self-consciousness or nervousness.

Probably the emails are not supposed to be proof, but just an interesting example, to say that after doing lots of research and discovering this trend, the professor was surprised to find their own emails following that trend.