The Doctor was pulling a con, on basically two groups of people:
Amy and Rory
Inviting Amy and Rory to his "death" allows the Doctor to prime them for two very important tasks:
- Guide him towards gaining knowledge of the Silence. The Doctor is in an odd situation where he knows information now that he needed to know then, which means he has to rely on Amy and Rory to prod him in the right directions without asking too many questions
- Take on the Silence without him. It's not controversial to say that the Silence are one of the Doctor's more dangerous enemies; there's a small list of people who have violated the sanctity of the TARDIS, after all. The Doctor knows that at some point in their 1969 adventure, he's going to be separated from Amy and Rory, and he needs them to appreciate the gravity of the situation they're in.
The Doctor has never been above using emotional moments to manipulate his companions, and Matt Smith's Doctor is no exception; that's basically the point of both "The God Complex" and "Amy's Choice", after all. Faking his death, and more importantly inviting Amy and Rory to witness it, is another manipulation towards a desired outcome: defeating the Silence.
The other thing it allows them to do is move on from him, which ties into the next group.
Remember that the Doctor wants to disappear at this point. He discusses this with Dorium's head at the end of "The Wedding of River Song" (emphasis mine):
Dorium: So you're going to do this, let them all think you're dead?
Doctor: It's the only way. Then they can all forget me. I got too big, Dorium, too noisy. Time to step back into the shadows.
Remember that the Doctor is deeply affected by several revelations he receives in "A Good Man Goes to War", from both Madame Kovarian and River Song (emphasis mine):
Doctor: What is [Melody Pond]?
Kovarian: Hope. Hope in this endless, bitter war.
Doctor: What war? Against who?
Kovarian: Against you, Doctor.
Doctor: You think I wanted this? I didn't do this. This, this wasn't me!
River: This was exactly you. All this; all of it. You make them so afraid. When you began, all those years ago, sailing off to see the universe, did you ever think you'd become this? The man who can turn an army around at the mention of his name? Doctor: the word for healer and wise man throughout the universe. We get that word from you, you know. But if you carry on the way you are, what might that word come to mean? To the people of the Gamma Forests, the word "doctor" means "mighty warrior". How far you've come.
He wants to disappear, to stop being such a negative influence on people. He's not the first person in history to disappear by faking his own death1.
It's also important to his own timeline that River Song be incarcerated:
- A lot of the information he gains about the Silence comes from the data files of the Teselecta itself (in "Let's Kill Hitler"). The Teselecta only has these files because they're a justice robot and killing the Doctor makes River the worst criminal in all of history. Changing the past so River doesn't kill him would create a paradox
- If she's not in prison for his murder, he can't be sure that she'd be on the Byzantium, and the events of "The Time of Angels"/"Flesh and Stone" may never happen, which would be utterly disastrous for history.
The other thing to consider is the fact that this is exactly how it was supposed to happen. The Doctor faking his death wasn't an attempt to cheat the Fixed Point, an there are two pieces of evidence:
- The Doctor appeared to start regenerating. With benefit of hindsight, we know that the Eleventh Doctor was the end of the Doctor's natural regeneration cycle. If he were dying for real in "The Impossible Astronaut", he wouldn't have had any regeneration energy.
- "The Wedding of River Song" showed us what happened when you try messing with fixed points in time, and it's pretty unequivocally bad. But none of that happens when the Teselecta is shot.
So the Doctor using the Teselecta to fake his death was the fixed point in time created by the Silence, and it always was.
1 Or maybe he is. Wibbly wobbly...