Vaibhav,
One factor is the process and the second factor is how much is your Damage vs Savings on no claim bonus.
So if your claim is lesser then what you gonna save on premium you are not gonna attempt on Insurance claim process.This stands true for Auto Insurance.

For Life Insurance, The problem is that the family is under shock on the loss of the loved one and then there is a procedure to get the claim.I
f Family of the deceased really need that Insurance money they go in for the procedures and where as well to do families just leave it. One common perception is that Life Insurance companies do ask for lot of paper work before they give the money so that people just leave it.If you look from the Life Insurance company angle they need to make sure that they are giving to the right person and also there are not getting cheated.Common problems are if a person has died of certian disease then Insurance company try to reject application on non disclosure of the disease at the time of taking the policy.

I agree. These public sector companies are not agressive in discouraging claims. They are better when it comes to the actual advantage of insurance policy.