DNA - Should the police keep records of us all

I used to think that it would be an excellent idea for everyone to have their DNA tested and for there to be a central DNA record. My thoughts were, that when a crime was committed the police would be able to find the perpetrator straight away.
If you have nothing to hide you have nothing to fear
BUT
I went to a talk from one of the world authorities on Forensics and
NO
"It would be a very bad idea"  he said
He explained
All of us have 2 parts to our DNA (one from Mum and one from Dad)
Quite often samples of DNA found at crime scenes are not pure, they are mixed with someone else's.
So, at the crime scene, one DNA could be A+B
and the other one, the one it is mixed with,  C+D
They are mixed together and so when tested,  the results might come up with B+C (or A+D)
So
If there was a central register, with the DNA of everyone in the country, they would look up B+C
and
It might be mine - a complete innocent who had never been anywhere near the scene of the crime.
They would claim they had DNA evidence that I had been there
FRIGHTENING