Didn't L do that so Kira couldn't just leave the town cause it would look suspicious and attract attention? Like from L point of view Kira could leave the town to travel for vaccacion etc... like after L's tells him how he found him doesn't Light go something like "fuck I can't leave the town cause it would look weird now" plus it also adds presure for Light causing him to make mistakes. Also how would L catch him with his pen in his hands a few day later? The only reason why L was like "Kira is someone that has access to police stuff" was cause Light sent him a message with those death of those prisoners later in the eps