All this type of DNA sampling tells them is who you are. There is no additional information they can glean from it. It's really no different than a SSN. So do you think your name is "personal information?"
Do you always fly off into a rage every time someone asks you your name?
"You have no right to know who I may or may not be copper!"
No, that's not entirely true. The OP was not just to provide DNA to prove or identify who you are. If that was the case, then it should be mandatory for every citizen to provide a DNA sample to a national database, and if there is any question regarding your identification, they could look it up.
The point of the OP is that people who are arrested are being asked to provide evidence for the government to prove you are implicated in some as yet unidentified past or future crime. Not everybody, just people who happen to be arrested, which is, in itself, not proof of guilt in any crime. This is way different.
You have no control over where your DNA ends up. You leave a trail of DNA behind where ever you go. Others pick it up and transport it.
Let's say you were some young professional living in Chicago, and decided to walk along the lakeshore during the Blues Fest and smoke a joint. The cops pick you up, arrest you, take your DNA, and then decide to drop the charges because it's your first offense, you're a local professional, and they don't want to waste anymore time on you. But now, your DNA is in a national database. 2 years later in another city you once visited, there is a crime and a trace of your DNA is at the scene. All collectible DNA is run through the national database, and because of your past dope smoking, your name comes up. The cops, bound to follow all leads, come to your office to ask you some questions. Nancy Grace gets a hold of your name, and your life is ruined (OK, the last part is a bit over the line).
If this is not what the cops will use the DNA database for, then exactly what is the point. Like you say, they have your fingerprints, SSN, picture, all physical characteristics. Why do they need DNA unless they are going to use the info to track down potential suspects. But, they only get people who have been in the system before, so they are just assuming you will be in the system again. This is wrong.