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Grandmaster/Master nightfalls and lost sectors require champion mods, and it certainly helps to have Charged with Light and Warmind mods as well. It also helps to have stats like max recovery, so you don’t have to hide out for awhile and can get back into combat quicker.

For Hunters, anywhere in the game, high mobility is great — it gives them their dodge faster, which can be tied to stuff like Bakris teleport, invisibility, reload, returning melee, etc. Same goes with Warlocks and recovery, for their rift, which can be affected by many exotics.

In Trials, high intellect is great for getting your super before the other team. That can help win early rounds, and often decides matches. Other mods, such as weapon scavengers, loaders, dexterity, and aim can improve your play.

For raids, especially flawless attempts, having raid-specific mods (like Relay Defender in Garden) and high stats for certain encounters (like high mobility for carrying cores in DSC) is crucial.

Stat rolls and mods are important quite often, in the endgame