Aizen
Absolute Sovereign
No, I think people should take them at their own discretion. Who knows what religious or moral beliefs DNA test might compromise. Also, the conspiracy theorist will start to believe the government just wants to get everyone's DNA on file.
If a person has doubts and they're not smart enough to take it, then that's THEIR dumb ass fault.
Governments around the world already do a good job of that by getting DNA from people at routine traffic stops, sometimes keeping the DNA on file even if the charges/case is dismissed. The police have even put children into the files.