Palpatine's plans involved intricate manipulation of the Jedi order. The chaos and doubt brought on by knowing of the Sith's return had the council making moves that they would not have made otherwise... Moves that Palpatine had foreseen as part of his plans. Revealing the Sith's return at just the right time was a crucial part of his plans. It wasn't a blunder of incompetence or an act of impatience. It was calculated psychological warfare.
In greater detail-
It's all about doubt. It wasn't until they knew the sith had returned that they knew they had been 'blind'. What else weren't they seeing?!
The inner turmoil caused by this level of doubt gave rise to paranoia so subtle, that they themselves couldn't tell the difference between intuition and unfounded doubt.
Without knowlege of the Sith's return, the risk of training Anakin would have seemed far less. There is a huge psychological difference between a scholarly understanding that the Sith existed LONG ago in the past, and knowing they exist NOW. Knowing they are blind to the Sith, they begin to fear what they would normally not fear, seeing things in the shadows, fumbling in the dark.
Like Anakin's fear of loosing Padme being the very thing that lead to loosing her, so was the council's fear of loosing Anakin to the dark side the very thing that lead to them loosing him. By pushing him away, distrusting him, and treating him like a timebomb, they gave Palpatine the opportunity to be to Anakin what the council had not been.
So what if the council had never been alerted to the Sith's return? Was the fear and danger they saw in Anakin colored by their own fear of the Sith? Was it their fear of him that drove him away? There is no way to prove a 'what if', but I believe this is what really happened.