Is it normal for law enforcement agencies to destroy evidence this quickly on "unsolved" cases?
Depends on the crime. I know of a number of cases where unclaimed, abandoned drugs couldn't be pinned on anyone and they were quickly sent off for destruction. If it's not going to be used to prosecute someone, and couldn't be returned to the owner because it is illegal then why hold on to it?
I've also seen people told by responding officers to destroy their own drugs in lieu of charging them because it wasn't worth the paperwork over a single joint or whatever.
According to local lore there was a murder committed many years ago - well outside of living memory - and among other items collected from the scene was an unopened six pack of beer or Coca Cola or something that was essentially just present at the murder scene. Allegedly the Sheriff's department are not allowed to destroy the evidence because it was from a murder, but there is zero chance that the murderer is alive to prosecute, that murder will ever be solved, or that the bottles will be instrumental in solving that crime. This example is given during training to ensure police enter relevant evidence, not just everything associated with a crime.