Compare it to spy, which is quite time consuming as it is. That just has fairly simple yes/no decision for each player - it's often just "leave copper/victory, discard all else" and once you've hit a 'leave it on top' for a player, that decision is unlikely to change.
For inspector, for each other player you've got to make the choice "Which of these 5 cards do I want to get rid of". That's a decision that's likely to take some consideration - I wouldn't be surprised if it took you a minute to process through 3 other player's hands. Then, once you play it again you've got to make a seperate decision on a different hand for each player. That's not even taking into account if you force other players through a shuffle. Playing a chain of Inspectors could make for a turn that takes minutes to complete.
Maybe I'm over exaggerating, but it just seems like it's going to be way way too slow to play - try playtesting with 4 players where inspector+militia looks like a viable strategy and see.
