?

Because they don't have Ji Eun's cell phone (it's with her body)?

lol you don't need her cell phone to do that. Pretty sure the cell provider she's with has to surrender that information to the police (and yes they have access to her text messages).

They can use the cell phone service to see who she contacted last

Oh. I see. Then I agree with you, it's stupid of them not to check that.

Because the police can't look into poeple's text messages whenever they feel like it, they still need a warrant to do that. At the moment they see it as a case of "adult woman, known for running away, ran away", they have no idea that a crime happend that's why they're not trying to get that warrant.