And why do you suddenly trust the government to properly care for / manage DNA samples when you don't trust it to do a single, solitary, good god-damn thing ELSE properly?
Now there is the real issue people should be concerning themselves with: not whether or not the government can and should do something, but whether or not the people we put into government can be trusted with that power (whatever powers given to government). It isn't the abilities, the technology and such that is bad, it is the intent use it is put to by those with the power. As long as citizens get off their asses and vote, and make sure that those who truly want to control everything in our lives (I'm talking about the far right here, people like the theocratic Dominionists) get nowhere near the center of power.
Don't worry yourselves with whether the government should have this ability, concern yourselves with WHO the government is. Do everything you can to keep the wrong people from getting this power, and you won't have to worry.