You have your reasoning backwards
In most jurisdictions, most serious crimes are not subject to a statute of limitations or have periods so long that for all practical purposes they might as well be. However, less serious crimes usually do have limitation periods that are meaningful. Sometimes they are broken into two categories, as in the UK, sometimes several categories with different periods, as in Germany.
See Why do statutes of limitations exist? for reasons why limitations exist. I’m sure you can see why it might be appropriate to have different limits for crimes of different seriousness - littering is in a different category of heinous to murder.