Why didn't L check for fingerprints or hair? Related to this: Death note handwriting check

A lot of DNA must have rubbed off on the Death Notes. Unless the Death Note has a rule about fingerprints or DNA, I don't see how this isn't a plothole.
When the Kira Task Force recovered the Death Note from Kyosuke Higuchi there is 2 things which contaminated any DNA evidence on the Death Note:


The Kira Task Force touched the Death Note to see Rem
Light was holding onto the Death Note as part of his plan to reclaim ownership (when his memories returned)


To my knowledge there is no way to tell "when" fingerprints or DNA first made contact with an object being tested as such any of Light's DNA found on the Death Note can easily be explained by his interactions with it when the Death Note was recovered.

Remember that the idea was to capture Kira and convict him in a court of law and DNA on the Death Note would be inadmissible due to how it was handled. This is why the police tend to block of crime scenes ensure that the proper Chain of Evidence is met. In some cop shows there are times that, when a seal is broken or multiple undocumented people handled a particular piece of evidence, it can't be used in court. 

Even if Light didn't touch the Death Note when it was recovered and L found Light's DNA on it, suspecting Light again after the 13-day rule seemed to show his innocence would not help L since up until now Light had been very cooperative in aiding the Task Force and they were all on good terms. He would first need to prove to the rest of the Task Force/Police that the 13-day rule is fake  thus returning to what I have explained here and then rule out any other way Light's DNA could have gotten onto the Death Note after it's recovery.