Wall-o-text, how I missed thee...
That there were "billions" of Terrans in the K sector as of the start of Sc1 is an overstatement. While technically possible to reach "billions" from a founding population of 32k over 200 years, it requires optimum and sustained conditions to be possible. Also, can it be said that all psychics are the same? Given the ability is somewhat latent in Terrans, some may have the potential but it may not be able to be translated across via assimilation.
Whatever the case, even if the chances were 99% of finding a psychic the story still has it that the Overmind didn't find or assimilate this potential until New Gettysberg. The reason is not elucidated as to why but one can only surmise that whatever the reason, it was not so simple a task for the Overmind.
Originally, it's unclear whether the Zerg are innately able to sense/be attracted to psionics since it's inferred that such interest in psionics is due to the Overmind's motivation for wanting to assimilate psionic potential from humans. BW more or less clarifies that it was always innate however...
It was not an economic based decision on the Overmind's part but an emotional one because it feared the Protoss psionic power. The manual itself says the Overmind was "greatly disturbed" and "on the verge of despair" before finding psionic potential in humans.
I've heard different things about this over the years. It's clear that her reintroduction in the Zerg campaign was due solely to author conceit, but not just because they liked the character but also because Metzen, at the time, felt that the Zerg needed a human lens to see the Zerg.
Of course she's different (not just in the physical sense), she's gone through an experience like no-one else has before. Terran Kerrigan was a naive individual who learnt, too late and with harsh consequence, a bitter lesson that changed not only her physical shape but her outlook on things. I like to think of infested Kerrigan as being the true human Kerrigan (one who has embraced the inner darkness she always knew she had), not the naive and repressed Terran individual we see in
Rebel Yell. Her development is quite continuous and not a random arbitrary change as you make it out to be.
You're probably right about that and it's ultimately to the given story's
detriment because the last two missions stick out as being far removed from the story the previous missions have built up. On a constructed narrative level, Kerrigan really needed to be involved in some capacity in those last two missions.
This all started because of BW's depiction of Kerrigan. Sure, the narrative and the characters do tend to bend toward making Kerrigan (the Zerg are also similarly made to be OP despite having no Overmind) better than what she actually is but at least it's consistently doing that throughout BW.
This natural evolution you speak of here would've been some interesting territory to explore in BW but it would've been too soon to implement after the Overmind's death. The Zerg needed to suffer a tangible consequence of losing the Overmind and whilst we didn't see it in the way you would expect, having them be dominated and used by some crazy, hybrid freak in Kerrigan for her own personal goals is a pretty good alternative option in retrospect. Hell, I would've liked to see this natural evolution occur in Sc2 as a response to Kerrigan's rule and that this natural evolution without guidance by a hivemind or overt control be the basis of the
primal Zerg, not the shonky tacked on version we got in HotS.
But it should've been on more even footing by the end of Sc1. Those hundreds of new sides are just as much of a threat to themselves than they are to others and given their close proximity, the Zerg would've been tearing at each other first. It's important to highlight this because one of the common themes in Starcraft is the strength found in unity. Given the Zerg had the ultimate version of this and was most successful with it, it needs to be shown that when they don't have it, that there's some bad shit to be in (just like the reverse of the Protoss progress in achieving unity)
Hah! Tell me about it. Raynor says billions were killed? Eh, peanuts really.
I would say the Overmind didn't really
need psychics, just that it really
wanted them badly. It could invade Aiur and it was seemingly doing well all without Kerrigan's direct help, afterall.