My own view on this (and yours may differ) is that the government has only a limited obligation to provide compensation to victims of crime.
One reason for this is that not all victims of crime are seriously harmed by their victimization. One of the philosophical bases for victims’ compensation is that the government is responsible for social welfare and needs to make sure all its citizens have a decent standard of living. The majority of victims of crime do not have their standard of living affected that greatly by crime. If, for example, someone steals my car, I am hurt, but my standard of living does not drop below the minimum standard of living that the government is supposed to (according to social welfare theorists) ensure. The government might have an obligation to help people who are seriously harmed by crime (for example, if someone burned down my house) but it does not have an obligation to provide compensation for all crimes to all victims.
A second reason is that compensation cannot really make up for most crimes. If a woman is raped, it is very unlikely that a payment from the government will make her feel that much better. She will still feel just as violated and she will still have just as many issues related to the trauma of the incident as she would without compensation. Morally, the government may owe her something, but in practical terms, compensation from the government will do her little to no good. Perhaps the government could provide her with free counseling, but there is no reason to give a straight cash payment.
My view, then, is that the government should provide compensation when the crime has made an important difference in a person’s life so long as payment can help restore the person’s life to the way it was before. However, the government does not have an obligation to pay for relatively petty crimes or to give compensation for psychological harms as those cannot be healed by money.