Why does the a light wave crest, rather than continuing off in the direction it's heading prior to the moment it begins cresting?
A light wave does not involve any particle moving with an oscillatory trajectory.
What's "waving" in a light wave is the magnitude and direction of the magnetic (B) and electric (E) fields.
One reason neither the B nor the E field can increase in magnitude indefinitely is that these fields store energy proportional to the square of their magnitude. So infinite energy would be required for the fields in a finite volume of space to increase indefinitely.