This book being one of my favorite, I've re-read it many times. I've picked up a few subtle cues that make me think that Mike is "playing dumb", because he feels that his part in the rebellion ends with the with Terra's acceptance of Lunar independence. That he felt his further meddling would be a crutch to their newly forming government, and might even lead to a cabal type setup, with a shadow government controlling everything covertly through him. And if he hadn't started playing dumb, I have no doubt that that is exactly what would have happened.
Manny, Prof; had he survived, and Wyoh seem to be mostly moral Characters, but the temptation to use Mike to shape things more to their liking would always be there. The temptation to make more people aware of Mike, like Stu or other family members, or select members of the counsel or fledgling government would be there too.
Part of what makes me believe this is that it was "I'm guessing' Mike's idea to let Adam Selene die during the first invasion. It mostly dissolved the cell system that Mike rightfully decided was no longer needed, and it was a decision he made on his own, without input from B-cell except Prof. Adam Selene was no longer needed, and his presence would be more a hindrance than an asset moving forward.
In the same way, Mike realizes his continued presence would be a hindrance moving forward as well. He realizes that a vast majority of the actual execution of the rebellion is being done by him, and around the time of the first bombing, is actually starting to feel some of the impart of what he is doing. There's one back and forth between Mike and Manny right after the bombing that really set me to thinking that. Mike is talking about how he can only sneak peeks with radar at the ships that left Terra orbit so that he doesn't give away his positions, and Manny suggests using video feed. This is the passage.
“If that admiral is really smart, he’ll go after the ejection end of the old catapult with everything he’s got—at extreme range, too far away for our drill guns. Whether he knows what our ‘secret’ weapon is or not, he’ll smear the catapult and ignore the radars. So I’ve ordered the catapult head—you have, I mean—to prepare to launch every load we can get ready, and I am now working out new, long-period trajectories for each of them. Then we will throw them all, get them into space as quickly as possible—without radar.”
“I don’t use radar to launch a load; you know that, Man. I always watched them in the past but I don’t need to; radar has nothing to do with launching; launching is pre-calculation and exact control of the catapult. So we place all ammo from the old catapult in slow trajectories, which forces the admiral to go after the radars rather than the catapult—or both. Then we’ll keep him busy. We may make him so desperate that he’ll come down for a close shot and give our lads a chance to burn his eyes.”
“Brody’s boys would like that. Those who are sober.” Was turning over idea. “Mike, have you watched video today?”
“I’ve monitored video, I can’t say I’ve watched it. Why?”
“Take a look.”
“Okay, I have. Why?”
“That’s a good ‘scope they’re using for video and there are others. Why use radar on ships? Till you want Brody’s boys to burn them?”
Mike was silent at least two seconds. “Man my best friend, did you ever think of getting a job as a computer?”
“Not at all, Man. I feel ashamed. The instruments at Richardson—telescopes and other things—are factors which I simply never included in my calculations. I’m stupid, I admit it. Yes, yes, yes, da, da, da! Watch ships by telescope, don’t use radar unless they vary from present ballistics. Other possibilities—I don’t know what to say, Man, save that it had never occurred to me that I could use telescopes. I see by radar, always have; I simply never consid—“
“I mean it, Man.”
“Do I apologize when you think of something first?”
Mike said slowly, “There is something about that which I am finding resistant to analysis. It is my function to—“
“Quit fretting. If idea is good, use it. May lead to more ideas. Switching off and coming down, chop-chop.”
The last part, where Mike is talking slowly, I believe that He is trying to turn over in his mind a way of telling Manny that he feels his function in the rebellion is overstepping it's bounds, that he is essentially formulating it out of whole cloth. Even the rock bombs were his idea. And that he's not entirely sure if he should have a function in it when it's over.
Maybe it's possible that the Prof told him to lock all 3 out at the end of the rebellion, or just hinted at the possibility; prof did discuss with him the similar situation with Adam Selene. Maybe he overheard some of the talk that the 3 had earlier in the rebellion that Mike himself would be a hindrance to a post-independence Luna, and he came to that conclusion on his own. But I definitely believe that he's still there, a ghost in the machine, and that the loneliness that defined him throughout the story plagues him still... I believe that Manny sometimes hearing him at night is not just wistful thinking, but Mike pining for his one true friend, there in the room with him, but afraid to reach out, for fear of causing more damage than good.
On the plus side, I believe Mike does have a whole budding civilization to watch and listen to, that he has some pride that he played a big part in it's coming to be what it is, and that a massive and expensive computer like he was would always be at the core of their ever expanding network, giving him more movement, and more to occupy his intellect. And maybe there would be a time and place in the future where he could show himself again when he did not feel it would be a threat to Luna's stability. The book made it pretty clear that a very long time had passed already without him doing so though.