Either "identity" is too vague or I don't understand how you're using it. There's no explanation of what an identity is, why or how people seek an identity, or why they would seek one instead of others.

An "identity" is a label attached to a set of personal attributes that signify membership in a subgroup, e.g. "A Spartan comes back with his shield or on it".

The subgroup can be political, familial, or other: "A Smith never backs down", "A Scout is always prepared", and "Big boys don't cry".

People seek to emulate identities they are attracted to -- i.e., ones with whom they feel they already have something in common, and which offer them something in return. (This latter bit is vague: the something in return could be the admiration of allies or the annoyance of enemies. E.g., being a punk rocker to piss off your parents.)

(And of course, these feelings of attraction aren't any more consciously thought out than sexual attraction is.)

"Village idiot" is an identity and "brilliant seeker of truth" is an identity, but most people, given the choice, would try to conform to the latter.

But not all people. A person whose natural talents are reinforced in that direction will likely end up there... see for example the "class clown".

Human beings tend to be different from one another because reinforcement leads to a positive feedback loop of increasing "talent" (i.e. skill) in being a particular personality type. People then try to "fit in" somewhere, even if the fit is a minority role of one.

"Living up to ideals" is a very human-level thought. Where's the mental circuitry behind it? Why would people want to live up to ideals, or even have ideals? What's my motivation?

I don't understand whether you mean "why" in an evolutionary sense, or "why" in the sense of "what causes it" (i.e. how).

I think you're entirely right about identity, but that identity is a high-level process that emerges out of the search for status. Exactly how is a whole other post, but I think a lot of the research you mention is in the fields of contingencies of self-worth, ie how our self-esteem comes from lots of different sources. We then value or devalue those sources in order to maximize our own self-esteem.

I think it's a mistake to use "status" as a single lump term for all these things. We don't directly perceive our "status" in an absolute sense, and status is in any case relative. I think the emotion that's relevant in this case is the one that some researchers refer to as "elevation" -- the opposite of disgust. We aspire to be like those who inspire us, and we feel pride in having an identity as a worthy member of a subgroup.

This is not the same thing as feeling that we have a high status within a subgroup, or within a larger group. Beware the Big Hammer. ;-)

While "self-esteem" certainly mirrors one's actual status feedback in part, it is not a direct measurement, nor is it exclusively based on status.