There are several questions floating around this interesting thread:
First, as Olivant said, the hearing was a Senate investigation, not a grand jury; and in the pre-RICO days, it was not, strictly speaking, against the law to be a consigliere. In fact, unless a specific charge was leveled against the Don or a member of his family, it wasn't against the law to be in the Mafia. In fact, there was no way to stop any lawyer from representing an accused person in any kind of proceeding unless the lawyer had been disbarred or convicted of a crime.
Second, putting Tom's photo in the chart as consigliere was an attempt by the committee to show his connection to Michael and his criminal enterprise--no doubt about it. But, if you look at the photo of the chart on p. 216 of Lebo's book, you'll see that there are no footnotes under Hagen's name connecting him to specific criminal activities, such as shylocking, drugs, criminally receiving, etc.--just a FBI file #. Presumably, if Michael had gone down on the perjury charges, maybe the committee and the federal prosecutors would have started working on Tom, Fredo, Rocco, Neri, etc. But Michael was the target at that point.
Third, Cicci had a choice: to remain silent and honor omerta, or do what he did, which was to break omerta. He told things about the family that were supposed to be secret. Even though he didn't directly implicate Michael ("I never talked to him"), he said that Michael was "the head of the family." That one phrase in itself could have damaged Michael's legitimate front.

Well I cannot argue with the fact that he broke Omerta. And we all know what the penalty for breaking Omerta was.

So in truth, FFC dropped the ball by not including Willie Cicci in Michael's quest to get revenge on all of his enemies.

Several people have made the point this was a Senate hearing, and not a trial. That being the case, the scope of inquiry is far broader, and issues like relevance do not mean much. The whole point of many of these hearings (aside from allowing Senators to grandstand) is to ferret out information about a panpoly of things. These hearings were about "the mafia" with Michael Corleone as the big fish. So why they would have Tom on their poster, and do nothing to besmirch him remains curious.

Exactly ONE of the points that I was trying to make.

Nor did he avenge the Rosato brothers. I've always felt that was the biggest "loose end" that needed tying up.

Good points, and no one can say this has to do with "cinematic license" or jamming the plot with too much storyline. A hit on Cicci and the Rosatos could have easily been shown montage style, as in GF I, and it would have nicely tied things up.

...especially since, in the penultimate boathouse scene, Tom mentions the Rosatos in the same context as Roth: "Roth and the Rosatos are on the run...do you have to kill everyone?"
Tom was exaggerating for effect at that point. But we could have inferred that the Rosatos were on the list--we just didn't get to see them whacked. The same might have applied to Cicci.

But we WANT to see them wacked!

I would imagine Cicci was doing time in a regular prison, so he may have been shot by a police officer, or hanged himself in his jail cell, or just got struck by a bolt of lightning.

Or a poisoned jailhouse baloney sandwich, a la Connie.

... or simply written out of the script.

Yeah. FFC could have given us a quick scene showing Carmine Rosatto getting whacked while celebrating his birthday in a restaurant.

Two shots to the head, and stick a C note in his mouth.