A few things
1. Though it is tough, I know I make a substantial effort not to be too biased by the game result. As a supportive example I believe the last game was very pro-mafia, even though town won.
2. You're underestimating the chance of tsims being caught. Suppose one person had a rock-solid alibi (1-2 rock solid alibis are pretty typical.) And suppose that a townie was elected police officer. I'll even count the the gay knight partner in the denominator. Then, the town has a 4/8 chance of immediately catching the mafia. And I think that's reasonably generous to the mafia.
3. Lucy wasn't a fluke. I'd say that there was an 80% chance that the mafia who attempted to kill Lucy would die in the attempt.
But I agree that the game is very sensitive to parameter changes. It took what felt like pretty small changes to (in my opinion) shift from mafia op to town op.
And I definitely agree that the town didn't win
because of their starting power. But I think that their starting power was
sufficient to win with high probability. They would
also probably have won with significantly less power because of how well they played.