My issue with the immortality operation thing is the fact that Law claims to have no interest in it, even though it has already been etablished that law was pretty much planing to sacrifise himseln order to buy time for the strawhats to destroy the smile factory in order to pittning Kairo against doffy. We know that was a pretty risky bet because it didn't work out as simple as he though, plus he had to go through the process of kidnappning Caesar in the process. If he was planing to sacrifise himself to avenge corazon, why didn't he just go to a yonkou or like sakazuki and offer immortality in Exchange for doflamingos head? That way he might also have been able to see some of that mayhem unleashed from doflamingos death, which was his big regret in the plan he decided to go with.
I mean if he was already prepared to to die in order avenge corazon, and he had like the most convenient bargaian chip at hands (immortality) why go for the more tedious and risky option (kidnappning Caesar and betting everything on the strawhats)?
WG and Marines can't attack Doffy because of his mysterious trump card.
But you're right about Kaido. Hum..maybe Law is the kind of doctor that respects life in a very specific way that prevents him from playing with immortality.