As clearly said by Krishna to Arjuna in Bhagwat Gita, that, "I remember all my previous births but you don't". Then question arises is why God only has that Extra privilege, and why normal human beings are deprived of it.
One may argue that why normal people need to know? If it is known, then at least people will understand the direct cause-and-effect principle.
Also people will automatically start behaving more humanly as they will know that if they misbehave, their next birth will be one heck of hell.
The memory from last births will act as a deterrence to avoid bad karma in current birth as humans are known to learn from their mistakes.
Now, when people suffers in current birth, and some sage or someone tells them that it is because of sins or bad karma of your previous birth, it becomes impossible for that person to digest it, specially if he/she does not believe in past life or reincarnation.
What could be the reason why God kept this seemingly obvious thing away from mere mortals?