We will just have to have different opinions for now. I think you are correct about Olivia meeting with Alexander toward the end of his life. For me, that doesn't infer time spent grooming, teaching and evaluating her. The fact that she might have made an effort to get along with him as his life was coming to an end seems more in line with a plan of Callista's. I could see Callista condoning a well trained and disciplined Olivia to spend a limited amount of time with her father in an effort to gain as much insight, information and understanding of the Karlsson Group as possible. If Alessandra got along with Alexander and learned that Olivia seemed to get along with him as well, it might be more likely for her to be the one to take Olivia under wing.
This is what I wanted to write, but something prevented me (perhaps my procrastination or tired eyes from lack of sleep)...I also tend to think that Alexander communicated with Olivia
in a limited way and gradually transferred to her the key knowledge about the Corporation and everything that she will need to know....
And he did it also because he put great hopes on Olivia, connected with the fact that Olivia was brought up by his lovely Callista and such a daughter (without Alexander's pronounced evil), and also stuffed with knowledge of both Callista and Alexander, will be able to roll mountains and at the same time she still has chances not to turn into a monster, as Alexander became..
So maybe Olivia is his last hope... And knowing that Alexander gave Callista strict conditions and made her promise that she would put Kane (when he grows up) in a rehab program, thus allowing Gambit to get started, this pairing of Kane and Olivia was most likely pre-approved by Alexander himself.
Yes, to him, our pairing of Kane and Olivia could have been something like Adam and Eve that could have started a new lineage, but Alexander, as the father of his daughters (albeit not the best), still gave them all equal opportunity so that the worthiest of them would win the fight (Gambit). As for Kane, well ..he's notoriously irreplaceable.. (at least as long as V keeps an eye on the state of his sperm, hehe).