The system will react to cope with this issue... primarily by holding off on the laying of charges for the primary issue, and either 'forcing' other charges on a suspect (irritate him and his family until he, predictably, retaliates violently, or in some equally criminal fashion, or simply framing him). 

Since police forces are action oriented, they will overburden themselves monitoring suspects who cannot be tried, and crime rates will rise as other police programs are deprived of staff.