You may be conflating shyness, social intelligence and introversion. Just for clarity, here are some definitions which I don't assume everyone knows.
Shyness "is the feeling of apprehension, lack of comfort, or awkwardness experienced when a person is in proximity to, approaching, or being approached by other people, especially in new situations or with unfamiliar people"[0]
Social Intelligence "describes the exclusively human capacity to effectively navigate and negotiate complex social relationships and environments"[1]
Introversion is "the state of or tendency toward being wholly or predominantly concerned with and interested in one's own mental life".[2]
When I was younger, I was told that all of these things were the same , and I was very confused. While I felt more connected to my inner world than the outer world, I had no problem dealing with situations (such as parties, events, etc) where I met a large number of people. I wouldn't actively seek these types of encounters out, but would navigate them (often with compliments) when they came up. However, afterwords I would feel physically and mentally exhausted. Only later in life did I learn a more nuanced view about introversion/extroversion that dealt with which situations one finds more or less rewarding.
I personally find small teams, often just me, highly rewarding and engaging. Afterwards I feel mentally recharged, and can continue such encounters for very long amounts of time. Conversely, I find that large groups are very draining, and I have to take more time to recharge.
I would generally rank in the middle-lower levels in shyness. I don't actively seek out encounters with strangers, but I do not feel a high level of apprehension or awkwardness. For social IQ, I'd rate myself as average. I can talk someone's ear off, understand empathy, and social situations do not generally throw me off balance. However, for introversion I'm near the top. Given any particular situation, I would prefer to be alone or in small groups, even to point of possible negative social/group consequences (which I generally understand and accept as the cost of the trade-off).
So while I agree with you that some introverts are pigeon-holing themselves, there are people, like myself, who value their introversion and do not feel that it is a limitation.
[0] http://en.wikipedia.org/wiki/Shyness
[1] http://en.wikipedia.org/wiki/Social_IQ
[2] http://en.wikipedia.org/wiki/Introversion
Edit: Typos