Ideally the team should've moved on to a new story with a similar feel. Use the popularity to create a series of self-contained 8-episode seasons. Become a brand not as a series of returning characters but as a mark of high quality crime I understand the wish to bring the two detectives back, though, as they were great performances. They could've had them moved to another place, quite naturally after the first season, although it would become forced if they kept on moving to new places for each crime. It was a hard job choosing direction after the first series, I get that, and as you say, they did have elements they could build upon, and the concept of s2 is not bad. But they lost sight of what makes the series good: the simple story and the attention to characters and the community as a whole, not twists and turns and implausible high octane confrontations.
S1 certainly walked a tightrope balanced between captivating drama and schmaltzy melodrama as well, but they stumbled with S2.
