So, to who was Michael illustrating his ruthlessness by murdering Fredo? Perhaps the answer to that is that once Fredo's murder circulated through the underworld, the reason for it would then have then become known. But, what would that have accomplished? What incremental fear of Michael Corleone would have ensued as a result? I don't see it. Compared to the enormity of fratricide, what advantage did Michael gain?
Logic is on your side, Oli. Then again, in the Mafia business, logic isn't always the figure of merit. Paranoia often trumps logic.
He got rid of Pentangeli and Roth because it was well known throughout the underworld that Pentangeli had betrayed (quite publicaly) Michael and the other wanted him dead.
No doubt those were the primary reasons. The Feds weren't going to give Pentangeli a free ride for the rest of his life without getting something in return. They'd have pumped him continuously. And, while his value as a witness was nil, he might have eventually given up something they could have used against Michael. Roth was simply too dangerous to live. As long as he breathed, he was a threat to Michael--look what he accomplished after suffering a near-fatal stroke and almost being suffocated.
But, the manner in which Michael engineered their deaths sent a message to his "enemies," whoever they were: Nothing stops Michael Corleone from exacting revenge. No one gets a pass.
