As with any information-related issue, this is not a simple one-dimensional debate.
On the one hand you have the possibility that you could improve the detection rates for many crimes. Clearly, this is of benefit to society and many may view the fact that they are unlikely to commit an offence themselves as a reason not to object.
On the other hand, you have a situation that would completely redefine the notion of freedom in society.
You have justifiable fears about scope-creep.
If I am an insurer, I am essentially a gambler. I am betting that the chances of someone costing me more money through making a claim are less than the chances of me being able to roll around naked in piles of fifty pound notes paid in premiums. If I can decrease the odds of a successful claim then I will. If I could use DNA to screen out people with a high chance of dying early and thus a claim against life cover, then I will. Is it beneficial to society that this happens, if it means many people left in poverty because they are unable to get insurance?
You have the potential for error or fraud.
On balance, I think it's okay to retain the details of the guilty, but not the innocent, and there are legitimate concerns about the present disproportionate representation of some groups - black men, in particular.
However, perhaps a more pertinent point is whether we can possible afford such a system, particularly given the wonderful success of other existing public sector IT projects of substantially smaller scale?