Alright, since you asked:
The choice of either destroying the base or keeping it relies on a single question, which, depending on the answer, determine whether or not you keep the Base, or blow it up:
Can you trust TIM with it?
Before you jump all over this one, this is a legitimate and valid question. Even if the base had anything worth keeping, you don't have the option to give it to anyone else, or deny TIM the ability to access it. So regardless of whether or not the Base has useful technology, you have to be willing to trust TIM with it. If you can't trust TIM, then you cannot in good faith give it to him to use, good intentions on his part or not.
This question is likely the primary reason Paragons blow up the base. Even if the base were to have technology that could be useful, they cannot trust that TIM will either:
- Not somehow wind up repeating the disaster that was the IFF mission (with the entire team being indocrinated)
- Use the base's technology for the goal of helping save the galaxy from Reaper harvesting
TIM's statements should you blow it up "Securing human dominance for the Reapers and beyond!" and "Cerberus IS humanity" obviously casts some doubt that his goals are anywhere near noble. I will not deny your argument that the base could indeed have useful technology or intel on the Reapers. But, with no sure way of guaranteeing that TIM won't possibly use it for something BESIDES stopping the Reapers, and your only alternative being to destroy the base?
Also, I realize that Shepard's arguments for destroying the base in-game boil down to the ethics of using the technology that killed so many people. While seemingly ridiculous, there is a legitmate reason for that stance. One of the reason research derived from the unethical experimentation on people (and sometimes animals) is viewed as "tainted", is because by using that research, you are (whether you believe it or not) condoning the method used to attain those results.
Shepard's argument is that, if you use the Base, you're condoning the rather nasty and gruesome death/experimentation of the colonists by the Collectors to obtain your answers. I won't deny that isn't a somewhat silly argument to make when the fate of the Galaxy is at state, but the Collector Base is just ONE item. It is, for lack of any other definition, a death factory. If the Base turns out to offer nothing, then that's valuable time, effort and resources you wasted on something that got you nowhere.
And I don't need to bring up the track record of what happens when people work closely around Reaper technology to say how that could turn into a really, really bad idea.