And yet he spends all that time arguing with TIM about it.
Because he doesn't think it is possible that the Reapers can be controlled. Controlled, as a specific word here. Up til ME3, the only known way to stop any Reaper was to destroy it, so Shepard went with that. But driving them into dark space is something. Or shutting them down. Or whatever.
And then when things got a bit more iffy and Shepard can even lightly speculate on whether the Reapers can be controlled (to be rebuffed by Hackett right after), control starts becoming an option, even if it means turning against most of those you work for and care about, for the sake of seemingly assuring the safety of them.
He argues against TIM because TIM is increasingly a madman who is actually working towards Reaper goals with each passing day, even if he can be argued to be resistant to it. Shepard's words, especially in the Paragon path, do no deny that Reapers can be controlled - but he does make the argument that TIM is not fit to do so, and to seek that path.
Then a Shepard who chooses Control in the ending is not doing so with a power thirst or confidence. In fact, he is (relative to Destroy stance) more weakened and defeated, giving himself up for what seems to be the chance to protect everyone and rebuild the galaxy as fast as possible, while there's still a galaxy left to rebuild.
Shepard can be seen as hypocritical here, but he can also (especially if he sticked to Paragon options) be seen as someone who takes in more info than he otherwise could have, and decided to act on a theory.
Eh we are just playing with semantics at this point. The Reapers were an obvious intergalactic threat. They made their motivations and ambitions rather clear when Sovereign explained to Shepard their purpose on Virmire. I'm fair certainly when Shepard meant "stop" he really meant "destroy." When did we ever see Shepard in ME1 or ME2 not destroy a reaper?
To try and suggest anything else because of the limitations of the English language is quite frankly ridiculous. Shepard had been hellbent on the destruction of the reapers before anyone else. The only one who really wanted to "stop them" was the Illusive Man, who just wanted to control them for his own ends.
When Shepard said "stop", he definitely did mean "destroy". I'm not saying otherwise, so please don't misrepresent me on this.
But he wasn't AS sure about it, compared to Renegade. By saying "stop", with his specific line delivery and conversational context, we're to understand that Shepard is open to whatever else could stop the Reapers.
It is just that the only one offering a solid alternative is TIM, and TIM is being depicted with increased insanity.
So Shep continues his default to Destroy. His friends want it, even his synthetic ones if he talks to them enough. His superiors want it, and they hinge their hopes on it. So he does the same, even as a Paragon who might question what TIM is really up to.
Shepard is hell bent on kicking Sovereign's ass in ME1, and destroying the Human Reaper in ME2. However, it is TIM's intervention (and the result of a crafted experience he was giving Shepard since the start of ME2) that gave Shepard something new for once - the option to keep Reaper, Collector technology instead of destroy it. Shepard can decide to do so, and this starts the path to at least accepting the existence of outright Reaper tech instead of the Reaper derived tech of ME2 earlier. That was Renegade because it was all with the intent of Destroying Reapers (Shep keeps this throughout ME2), but it also means that both Paragon and Renegade players in the ME2-ME3 run have experiences of accepting the presence of Reaper Tech to some degree - either as tools or subjects (but generally tools).
Then ME3 happens. Shepard wants the Reapers dead. He wants them gone. But there's the nagging bits that come from both learning more and more about the Reapers (which DLC can also help in adding to), and TIM's insistence that Shepard isn't seeing the bigger picture. Shepard never agrees for 80%+ of the game, but he can be given the option to wonder.
So we're eventually told that TIM was right, at least in his own way. We can act on the information we've acquired throughout the series and try out Control despite its dangers, or we can stick to the goal and Destroy, which comes with its more definite drawbacks (of varying degrees).
Synthesis exists as an utter leap of faith, as we have absolutely no solid evidence that it is good. Enjoy the green circuited dream. Synthesis is good for the Shepard utterly worn down by death and just wanting something great to come from it all, or the Shepard who has saved as many as possible (plus curing Genophage, Rannoch Peace) that wants to continue his galactic savior-ness into its conclusion, even if it means acting alone to do so, and possibly being delusional about it.