At a glance, you might expect Spectrier to be a pretty scary Pokemon, with its 145 base Sp. Atk, 130 base Speed, and spammable Ghost STAB, and it probably would be were it not for one major caveat; Calyrex-S exists and does almost everything Spectrier does, but better. There's almost no reason to use Spectrier over Calyrex-S with two notable exceptions.
The first is using Spectrier in conjunction with Calyrex-S; Calyrex-S is considered an alternate form of Calyrex, not Spectrier, so species clause does not forbid the use of both on the same team. Together they can be used to form a pretty scary Ghost-spam core that can wear down an opposing team's Ghost resists, but there are other Ghosts that generally fulfill that niche better, such as Blacephalon, Marshadow, and Lunala.
The other small niche is that Spectrier's pure Ghost typing can allow it to lure in defensive Yveltal, Burn it with Will-O-Wisp, and then use it as set-up bait. This plan falls apart if Yveltal has any dark move besides Foul Play, and can't touch anything that can handle boosted Ghost-type moves (such as Blissey and Arceus-Normal), but it's something... I guess.
In reality you're almost always better off using Calyrex-S over Spectrier.