There's no need to mock a culture that's different from your own. 'True American theatrics' indeed... Get over yourselves. The sniffing is a tic of Supt Carter. It wasn't an attempt at drama - you can hear it in several press conferences he has given, probably thanks to allergies. The very clear personal commitment on his part to the solving of these murders, his updates over the years, and his determination to find the killer has been a key part of the investigation, and the publicity he has given to the case has very likely been responsible for the huge number of tips that have come in.
It's a rural community, with farming families that have known each other for generations. Delphi has less than 3000 residents. The two girls had their lives snuffed out, and the murders have affected the community deeply.
And fwiw, detectives executed a search warrant on the suspect's home on October 13th, spending hours searching through the home, and removing items from inside, as well as Allen's vehicle. They also dug some trenches in the back yard of the Allen house that night, and appeared to use a metal detector in the area. Allen was arrested on Wednesday, charged with two counts of murder on Friday, but the charging document remains sealed and the investigation is ongoing.
There will probably be a hearing some time in the future to determine whether the charging documents can be unsealed, presumably with news organisations petitioning in favour, and depending on the status of the investigation the prosecutor arguing against.