Detective: City of Angels - rotating the Chisel player?

Is it better to use the same player as the Chisel for every case or can players rotate who fufills the role? I know the Chisel needs to play the case before, and I can easily lend the game to whoever's turn it is to Chisel.

My group has been playing MindMGMT with me as the Recruiter, and while that's been great it's kept me locked into the role. Would love to give each player a chance to Chisel if it's a reasonable thing to do!

Bonus question for fans of the game: Which Expansion is your favourite? Which would you recommend after finishing the base game cases?