Even though the Doctor is a time traveler, he still has a finite existence. By killing him you ensure that future versions of him can't meddle with events. And really, playing dead so as to exist under the radar is only relevant to certain large groups that already know who he is. The Silence, for example, are probably aware enough of his personal timeline to know which version of the Doctor they need to worry about.
The Doctor, as far as they know, died on Lake Silencio. If somebody tries to kill him before that happens, they will fail, so it's not even worth it to worry about earlier versions of him. Since it's pointless then to worry about the Doctor before Lake Silencio (because he obviously survives those encounters) and it's pointless to worry about the Doctor after Lake Silencio (because he's "dead"), you now have a universe where nobody needs to bother seeking him out at all.