Catherine the Great never intended that her son Paul—weak, mentally unbalanced, and ineffectual—should succeed her. Instead, she favored her grandchildren, particularly Alexander, who was both bright and competent and shared her understanding of and commitment to rational government.
If you have enough power you can do whatever you want. The Tsar certainly had enough power to declare anyone they wanted successor.
First of all you should realize what were the patriarchal "father-son" relationship of Russian peasants of that age:
An old father is sitting by the window and sees his son entering the house.
Son: "My Father, you seem angry. Did I displease you?"
Father: "Yes, my son. I want to punish you, but I am too weak and I need that big stick over there to give you a proper beating. Give me that stick! Quick!"
Son: "Here you are, Father. Take this stick and beat me. But be careful, don't try too hard, I am afraid that this effort might hurt your health".
Of course the above was kind of ideal situation. In real life there was sometimes a son who struck his own father. Well in this case the son was taken by authorities into the Central square and the son's hand was cut off. In a clear sight of approving crowds.
Why am I telling you this?
Because 99% of the Russian population shared this mentality:
" - Father is the head of the family and his son(s) must obey him."
That was a cornerstone of the traditional Russian patriarchal family and all Russian life in general.
So if Catherine the Great keeps her son Paul alive but appoint his son (her grandson) as her successor... well, when she is dead, Paul goes to the nearest Russian regiment and says to the soldiers: "You see, guys, I feel mistreated by my Mother. I think that the throne belongs to me. It is wrong if son is on the throne when his Father's alive"
Every Russian soldier feels that Paul is right. And I mean 'every soldier'. And they declare Paul the tsar/emperor.
If there are some officers who disagree with Paul - they are butchered on the spot by the soldiers. The same happens with all military units.
A few days later the Empire belongs to Paul.
end of story
So the only variant for Catherin the Great was to murder her son Paul in order to make certain that her successor would be Alexander or any other her grandson.
I think she seriously contemplated this decision, but she did not make it.
It was too tough, even for her...