How much of the swinginess of the game comes down to whether the hatcher hatches?
The Hatcher is arguably town's strongest role; having it hatch early in the game can give town a nice head start on hatches. But mafia gets compensation if town has a lot of hatched players, and more town won't hatch if the hatcher successfully hatches many townies. Say 3 town roles hatch N1, including the Hatcher. In a scenario where town is exiled D1 and D2, unhatched town dies N1, and the Hatcher targets town N1, that leaves us with 8 townies at the start of N2, 4 of whom are hatched. Town won't get any more automatic hatches, but mafia will. In testing, correct Hatcher targets really just mean that town gets its hatches sooner (which is good for town), but mafia gets more roles to counter those hatched roles. Additionally, the Hatcher can target Mafia, which kind of negates that advantage to town.
Edit: on the flipside, if the hatcher never hatches, town will get more automatic hatches, it just happens a little slower.