Local law enforcement should not just enforce the law of the specific city they are in. They should enforce all applicable laws: city, county, state, country, etc.
[1] “The clause relating to fugitive slaves is found in the national Constitution, and not in that of any State. It might well be deemed an unconstitutional exercise of the power of interpretation to insist that the States are bound to provide means to carry into effect the duties of the National Government nowhere delegated or entrusted to them by the Constitution.” Prigg v. Pennsylvania https://supreme.justia.com/cases/federal/us/41/539/
[2] “Congress may not simply ‘commandeer the legislative process of the States by directly compelling them to enact and enforce a federal regulatory program.” Murphy v. National Collegiate Athletic Association https://www.oyez.org/cases/2017/16-476
This is not the case when you consider the relationship between the states and the federal government, though. While the states obviously aren't fully sovereign, the federated structure of our country explicitly grants them limited sovereignty that is innate and not in any way derived or subject to the federal authority. Thus the ability of the federal government to commandeer state governments to its own ends is rather limited and needs to be explicitly spelled out (e.g. National Guard can be federalized, but State Defense Forces cannot). And last I checked, there are no clauses in the Constitution that give the feds the power to commandeer state law enforcement to enforce federal laws; nor did the courts find such power implicit in other clauses.
Not only shouldn't they do it, they _can't_. You don't want some local sheriff deciding you're guilty of, I dunno, securities fraud, and you don't want the FBI writing parking tickets.