I remember reaching back when COIE was first concluded that DC felt Power Girl was more popular than Supergirl and they opted to keep her as part of the DC Universe and not Supergirl. SG's book was cancelled and would only be a supporting character/guest star anyway. So DC decided to keep the one they felt the fans liked the best.
Keep in mind that plans for Crisis changed several times. Originally all the ones at the Dawn of Time were supposed to remember the parallel earths. This altered and it was decided there would be no mention of any parallel earths. Plus, DC decided to completely reboot Superman. There was even talk or a suggestion by Marv Wolfman that DC restart all DC books with a new #1, indicating a new beginning for them.
I think the plan was for Power Girl to be the Supergirl on the merged earths. That's why the adult Robin and Huntress were killed off, as well as the Earth 2 Green Arrow. All the doubles or children of the doubles were killed. If DC hadn't decided to reboot Superman they probably would have ended up calling Power Girl Superman's cousin.
But Byrne rebooted Superman and stated Kal-El was the sole survivor of Krypton. So Power Girl couldn't have been Superman's cousin. They came up with a new origin and background for her, then yet another one. Only after policy shifted again were they allowed to mention the parallel earths again, which allowed them their now claim of her being the "last survivor of earth two".
Sure, Crisis changed many times, but the final issue that saw print saw Power Girl survive. And, then she survived the JSA one-shot after that, a strong indicator that there was some kind of plan for the character, it just seems too deliberate beyond wanting to make her the official "Supergirl". What I imagine was that Roy Thomas might have had some plans for her, but fell through or was nixed as he was constantly having to revise his plans for his titles as DC changed what they told him (such as still having Earth-2 to play with for purposes of All-Star Squadron). I would imagine that originally he thought he'd still be able to reference the old histories, that Fury was daughter of a Wonder Woman no one remembered and such. And he might have originally planned on playing on that with Power Girl as well. But, then given the mandate no references to the old histories, he sidelined Power Girl as he introduced the GA Fury and came up with a new backstory for the Infinity Inc Fury.
THEY knew Byrne was revamping Superman, they told him to! It's part of the reason we got Moore's WHATEVER HAPPENED TO THE MAN OF TOMORROW comics. This means there were some long term plans in place revamping Superman. He's on record saying he was willing to work with Superman as he was but they wanted a complete fresh start. Of course, like with Thomas, they changed the parameters of what they told him. Originally, his Superman (and Wolfman's) run would have occurred on the heels time-wise with MAN OF STEEL. Much like Perez did with Wonder Woman, it'd be about a new to the job superhero. He's on the record saying that he might not have gotten rid of the Superboy history otherwise. But, they knew for some time that there would be no new history for Power Girl to link in to.