Peter was an idiot who was destructing the Russia (give him more time and this will be the most likely result) being practically the president of the "Frederick the Great and Prussia" fan club and this was well clear at that time. True Catherine has not any claim to throne of hers, then you need first take care of Peter then put the rule in her hand as mother of Paul...
For the love of God, no one is arguing against the idea at Peter was the worst thing to be seen since Batu Khan or Ivan the Terrible or Charles XII or whatever you want to name.
What does that have to do with anyone putting Catherine on the throne?
And there's no reason why her as Paul's mother automatically gets to rule in his name unless there's some Russian custom I've missed.
And as Constantine said Catherine at that time was in Russia for many years (at that time was already more than half or her life) and was surely seen if not Peter the Great's at least Empress Elizabeth's spiritual successor and I think this was more than enough...
At the time of the later revolts, faux Peter III's supporters had almost surely forgotten how disastrous his policies were (or they know he was not the true Peter)
At that time, Catherine has been pious and respectful to her credit. That's it. Nothing that is going to make people break her out of a nunnery to install instead of her son.
And for (hopefully) the last time,
stop with how Peter was horrible.
As stated in my post above, repeating that is just avoiding addressing the issue of why Catherine.
Because Catherine has been, quoting
The Romanovs: "dutiful and reverent in her observance of Church ritual" and "calm and dignified, even in the face of the gross insults Peter heaped upon her in public"?
This may win sympathy, but it doesn't mean people will rally behind her to make her Empress in her own right over putting Paul on the throne.
My apologies for being a bit rude, but when no one is disputing Peter is disliked intensely, bringing it up again and again and again as if it somehow addresses an entirely different matter - why this replacement and not another - is irritating.