Do free Coven weekends actually hurt the game?
I have no statistics for this, but here is my reasoning.
1. It gives false impressions of the game
During free weekends all Coven modes will fill up quickly as players want to try them out, but usually some modes will be dead or will take forever to will up outside of "peak hours".
While this isn't bad for sales, it can lead to players feeling deceived, giving bad reviews or quitting the game entirely.
2. It highlights Covens problems
Coven has many problems. Some have to do with a lack of balance or some roles feeling lackluster in certain modes. Some have to do with more roles solely relying on RNG.
VIP for example is a mode that can easily be ruined by a single player making bad decisions. During free weekend this is often the case, as new players have no understanding of the mode.
Having these problems so exposed may lead to players thinking Coven might not be for them or be simply unbalanced and RNG-heavy (which it might be).
3. Classic modes might suffer
Obviously a lesser problem, but during the free weekend classic modes like Dracula's might not fill up, as most players want to play the limited thing.