Ah, but it WAS spotted. The problem was that the captain had ordered top speed through a known ice hazard area, so by the time it was spotted, there was no time to miss it.
Ironically, had it impacted the berg dead-on, it would not have sunk.
Which was probably the idea behind the whole set-up, since the "Titanic" that sunk was actually the Olympic that was previously damaged. Had it smacked the berg straight, the forward sections would have crumpled but the ship would not have flooded over the sequential compartments that the side-rip allowed. Then the claim that the ship was "unsinkable" would have been proven, and they would have collected the insurance money for the "Titanic" for icebergs that they couldn't have collected for the Olympic simply smacking into another ship through negligence.
But they had really GOOD lookouts that night, who were on the ball and spotted the berg JUST far enough out to avoid a head-on collision, and enable the slow turning of the ship to juuuuusst rip along the side...
The matter of the rate of Titanic's speed is interesting. J. Bruce Ismay, director of the White Star line is often depicted as the villain in the whole affair. Such was the case in James Cameron's film portraying Ismay pressuring for a record.
A view to the contrary suggests that his demonetization came about from William Randolph Hearst.
One way or another, the fact that this was Captain E.J. Smith's "retirement" trip has long intrigued me. What a terrible way to wrap up what had been such a distinguished career.