"no matter how much your influenced by a genre if you don't play that sound your not a part of that scene" When it comes to Goth that rule really get's pushed aside. A prime example would be Sopor Aeternus. Many people in the goth scene wouldn't flinch if you labeled them a goth band. Despite the fact that they sound nothing like Bauhaus. Nor do they share similar influences. Yet, Sopor are still considered Goth. This happens a lot within the Goth scene. The whole argument of a band having to "sound like a goth band" only get's thrown out there when the scene wants to distance itself from something they deem too mainstream or is associated with a group they see as "undesirable" (i.e. metalheads, fans of Marilyn Manson). My argument isn't to say goth and metal are the same. I'm saying that there's definite over lap between the two in terms of fanbase, influences, and in aesthetic. Which a lot of Goths aren't willing to admit because of the previous reasons listed.
"Many bands don't write music to be part of a certain genre or "scene" - they just sort of end up there because they play in similar styles and take influence from similar bands."- and isn't that what defines a musical genre? Someone started to play music in a certain way and influenced other artists to play in a similiar one. In the long run this creates a "scene" of bands with a similiar style and fans who like them, because of how they sound.
It is true that some metal bands had strong goth influences- but they are still metal not only for the fact of having different musical origins, but their sound isn'tmostly liked or shared among the gothic community. Even the gothic metal bands like TOF and Paradise Lost, who have the strongest goth influences, aren't related to the goth genre because of their fans coming mostly from the metal scene. And these bands also have their identification with the metal scene and probably influenced other metal (and not goth) bands as well.