here is my version of answer for why 14 years vanvaas..
i have seen a film in my local language in which it was mentioned that if a king or a person who is gonna be the next king leaves the throne and kingdom for 14 consecutive years then he has no right to be the king forever. that is he cant claim his kingship even after he comes back from exile. that is why kaikeyi puts the condition for 14 years.
now the question is ram left for 14 years but he became a king after he returned??
and the answer is
though ram was away from the kingdom for 14 years but bharat never became the king in his absence and he ruled the kingdom in the name of his brother ram by keeping his chappal on the throne. so it means ram was the king for ayodhya though he was not present their physically. so when he returned back he was eligible to be the king of ayodhya and hence he was coronated as the king..
coming to life sentence of 14 years i guess 14years is a long term in ones life. if person completes his 14 years life term then almost half of his productive life is lost in jail and he will not hold any grudge or revenge against anyone after he completes that. so that is why he is left out after 14 years.
eg: imagine a person of 30 years sentenced to life term then he is released at an age of 44. by that time his most productive life is lost and he needs to start from the scratch to lead his life so he will concentrate on his life rather than avenging on others.
and it is also believed that any thing in any person's life will last for 12 years. and everything will change at the end of this 12 years it may be love hatred revenge or even success too sum times... so the revenge a culprit has will almost be lost by this 14 years term and hence a new person comes out of jail who will be all set to begin a new life