If they cannot prosecute because of the statute of limitations, then there is no other reason to keep the evidence, unless some legal controlling authority had mandated it.
I can only imagine how much the citzens of LA pay every year for evidence storage. It must be astronomical.
What about future crimes?
Statutes of Limitations do not apply to police investigations, to prosecutions or to prosecutors.
They provide "outs" for those being prosecuted but must be exercised by the accused.
Seems to me pretty darn cheap insurance that we keep evidence of crime permenantly.