There was too much at stake to risk that TIM's ability to control (when we know that he's been playing with Reaper tech and has been indoctrinated by them and is controlled by them) is somehow totally different than their's particularly when we also know that if Shepard chooses "wrong" the Reapers lose everything and are destroyed utterly.
Being logical requires being absent of emotions. TIM's ability is not the same as Reaper's ability, regardless of that is at stake. Also, Catalyst says that Shepard will control the Reapers. If you believe him that it is possible to kill all the Reapers, why wouldn't you believe what control is possible?
Also, if Shepard was in the geth consensus before, he will address the problem, and the Legion will respond what it isn't problem for the geth technology.
Where will his/her sanity be? What guarantees will anyone have that contact with Reapers minds will not change/corrupt him/her?
In the same vein, it is possible that Catalyst was correct, and removing the Reapers will create Synthetic singularity and organics would be wiped out.
However, does that happen because now, that would require that synthesis would also have to change inorganic elements, too, to make it impossible for new organic compounds to form without forming in violation of the new framework
Well, that's one of the problems with Mass Effect. And science fiction in general. The universe is SO HUGE that our brains are incapable to truly comprehend it. Shepard and even the catalyst seems to be concerned only with Milky Way Galaxy. So I guess, we should remember that it is just a fictional story and accept some mistakes.
Personally, I was more offended with tiny stars which are sometimes smaller than their planets. What was annoying.