Keep it.
The tech that we have is based on reaper tech, tech which funnels into a certain progression that makes us easy to harvest. (Culminating into what I suspect to be the creation of a representative reaper for that species, but for what reason and why? Maybe the dominant species for that period gets a place in the annals of history as a reaper?)
We have utilized this tech not only through direct use but also modification, and have had minor gains against the reapers with it. Now we have access to a large resource of potentially new tech, which can be dangerous or beneficial, and useful or useless. This tech was not just left for us by the reapers, I would argue, since it was shooting everyone out of the sky and harvesting humans to build a reaper.
With the knowledge that a force that has never been stopped (to our knowledge) is coming to obliterate every species in the galaxy, I could not choose to destroy this potential resource.
Thoughts on earlier posts?
-TIM gets this ship and uses it.
Big deal. Whats he going to do? Start driving around space abducting a single species? Doesnt seem like it would sit too well with anyone, even in the traverse, He probably couldn't even get it out of the galaxy core. You can't just fly one of these things in colonized space without getting noticed. And say he does use it, my shepard benefits from the boost and has a greater chance against the end of the world. And if he tries something with it afterwards? I've taken down Cerberus before, an asari matriarch, a spectre and countless mercs and mechs. I'm confident enough to believe I can handle TIM if I can handle the reapers. Plus, might as well milk the cerberus cow as long as you can. Doesn't seem like many other private operations can handle your bills.
-EDI already hacked all the info out of the ship already.
More of an assumption than anything, EDI never mentions that she is doing anything of the kind in the last mission. Remember the first time she interfaced with the ship and had to deal with so many viruses she couldnt get a platform moving? Now she has a half-broken normandy to fly, coordinate repairs and keep relatively hidden. I would imagine that datamining the collector ship would alert it to the normandy's location. And the image of the reaper on the infamous datapad? Could be from anywhere, even schematics from the derelict reaper chananda was investigating.
-Give the ship to the alliance.
You're kidding, right? The alliance has done nothing but sit on their hands with this issue. What makes you think that they simply wouldn't discount reaper influence and put the ship in storage for "investigation" by "top men"? Who? "Top men". The council will still argue they need proof, and this is not irrefutable proof that the reaper threat exists. Plus, you worked for cerberus. Why would they believe you?
I just wish my renegade shep (first playthrough) didnt get so much flak from my entire crew at the endgame. I seriously feel like rodney dangerfield. No respect, no trust. Less grey, makes me second guess myself.