Or for those who are not scaremongering for the tabloids...

You're still innocent until proven guilty. A burglar cuts himself at a crime. in a hurry to get away.

Now: police have some blood. Big deal. If they happen to stumble on the person they might get lucky
Or: they compare the DNA to the records. If someone comes up they could interview the person quickly, not hope that the criminal suddenly decides to give up. Perhaps there is even such things as stolen belongings at their house.

The use of DNA obviously depends on source: DNA from a urinal proves nothing useful; DNA from a place that the individual had no place being is far more useful.

That juries are ignorant / easily led should not mean evidence is inadmissible as the jury is too stupid. That is what the judge and lawyers are there for. If the current system can be derailed by something this basic, it should be overhauled.