Grinding off a serial number is not only omitting another crime but also wouldn't necessarily prevent tracing the gun back to a crime with that firearm.
"Omitting?"

There's that phrase again: not necessarily.
Nothing is guaranteed, but it's more productive to discuss the vast majority rather than continually muddying the waters with rare or unlikely outcomes.
If that gun was used in a previous crime, why is it now on the streets again? Did a Cop steal it from evidence and obliterate the serial number as a "throw down?" Maybe he needed a "clean gun" to commit a crime that couldn't be traced to him or the department? Who has access to "guns used in crimes" other than the police?
If someone commits a crime using a gun, chances are they are now felons, unable to reclaim their gun. If they owned it, it probably gets destroyed. If they stole it, it may be returned to the owner. What are the chances the same gun gets stolen and used in a crime twice and THEN a third time with the serial number removed?
Just wondering why you think a gun with a removed serial would be in a criminal's hands. If the same gun was able to be traced "back to a crime with that firearm," how would that even work exactly?