I never keep the thing intact for 3 reasons:
1) I don't trust TIM - Even without the metagaming. Mass effect 1 gave me plenty of reasons for not trusting cerberus and I only worked with them because the game forced this decision on me. And all attempts that he and the rest of cerberus tried to convince me otherwise felt flat, and their true nature always come up in some way or another.
2) Indoctrination. Every artifact that has some connection with the reapers is a liability. I know that the history conveniently ignores this wen it needs (All the surviving squad should be at risk of indoctrination just for going inside the thing twice and also, inside of an ACTUAL reaper.). But still, I'm roleplaying, and because of that I don't take writer's liberties in mind.
3) I don't know the exact extent of TIM's resources, and the only source that could tell me (EDI) says that all cerberus cells work individually from another and don't know exactly what they do and how they are funded. The only thing I know is that they have enough to fund absurdly expensive projects like Lazarus. So even if I had the option to say "I will give it to the council/alliance" or lie to him, what's to stop him from ambushing me the minute I step out the Omega 4 relay? At this point, even with the upgrades, the Normandy has some serious structural damage, and I don't know jack s-hit on how to operate the collector base.
So, yeah, there you have it ;P