Putting 3 Police on a LoC (well, a total of any 3 COIN cubes+SF really, but the other types are more useful elsewhere) means that the Guerrillas become Activated if they try to move onto (as opposed to across) that LoC. This means that they can't use that LoC for zero-cost March+Ambush combinations.
During the Coup Round (6.2.1), having at least as many COIN units as Guerrillas on a LoC prevents those Guerrillas from Sabotaging that LoC (as long as all Cities adjacent to the LoC have COIN Control, that is). For the ARVN, it is quite useful to have a source of Resources that the US can't spend at will...
Great explanations of how to take advantages of Police onto LoCs.