$3,000 will buy you a whole lot of DNA testing and screening, so your scenario doesn't carry much weight in the cost-benefit analysis of the crimes that would be solved and prevented by sampling prisoners and arrestees.
Okay so I made up the dollar figures. Completely irrelevant.
The cost in the cost-benefit analysis of the crimes that would be solved and prevented by sampling arrestees (I have no problem with taking samples from convicts) is *not* $3000. The cost is the unconstitutional seizure of a part of my body.
Sure it would help prevent and solve crimes. So would random (and not-so-random) searches of private homes without the need of search warrants. Can I assume you believe cops should be allowed free reign over private residences in the interest of community safety?
(Here's where you say "no".)
Then why should they have free reign over my body?