Actually, if you early apex, chances are you're going to run wide at the exit unless you sacrifice your exit speed significantly.
“If the signs point to an early apex (or another problem), you have to instantly switch your concerns from driving through the corner faster to driving away from the corner with the car in one piece.” - Carl Lopez (author of Skip Barber Racing School's manual)
Although, depending on the track (for example if you have a long straight, followed by a sequence of 2 close turns) you can early apex to maximize your time on the long straight, and since the next turn comes up right away, your LOWER speed is of no consequence and it can lead to an overall quicker lap (since the time spent under full throttle of the preceding straight is more valuable)
Of course, in a racing situation, an early apex can be a defensive move to protect track position as well. And really, wheel-to-wheel, there really is no set line.