From having sat on a criminal jury in the U.S., the opposite seems to be true: jurors wonder why the police didn't DNA test a small stolen object to "prove" it was held by the accused. There was no reason to run DNA (the object was found in the accused's possession, etc.) and it's not even clear that there would be any DNA to run (fingerprints would have been more likely), but it seems like jurors have come to expect CSI level stuff in every case. Instead, most cases seem to still be done on old fashioned eyewitness testimony and circumstance (the stolen goods were in your apartment, you were also around the place where they were taken...).