First, I think they are inconsistent with the purposes of statutes of limitations, especially when used in prosecuting property crimes. The underlying reasoning for such statutes is along the lines of what the defense attorney talks about here: actions which satisfy a statute of limitations (at least theoretically) are usually meant to be those that clearly identify the nature of the charge, and the person charged, in a way that will “ordinarily” come to the attention of the accused.

The idea is that the defendant is allowed to prepare a defense before exonerating evidence is weakened with age (witness memories, his/her own memories, availability of things like cell phone records, other physical evidence, etc.) *because* a warrant is meant to be promptly followed by an effort to obtain the person, who is ordinarily seized in a reasonable time, etc. A warrant like this doesn’t immediately authorize the arrest of anyone: who knows when the DNA will be matched to an actual person that can be apprehended. It doesn’t really have any effectual significance until some undetermined future point, by definition.

A statute of limitations concedes that there’s a balance established between A) a state’s interest in arresting a person for a particular type of crime, and B) an interest in allowing that person to build a proper defense, and C) the state’s interest in clearing ts own cases.

If the crime charged is one on which there is a statute of limitations, then it seems to me that a warrant for a particular instance of that crime which can’t actually be acted on within the statute of limitations is, by necessity, inconsistent with that balance: the state’s interest in arresting a person conveniently trumps the other two.