influential bands =/= proto this or proto that bands
It depends on the level and kind of influence. No definite answer there.
For example, what do you think about Celtic Frost/Hellhammer regarding death and black metal? Both bands definitely provided strong elements that became key songwriting/production staples of what came after them. So, if they aren't considering full death/black metal bands they at least deserve the proto- prefix.
Now, Mercyful Fate and Morbid Angel have been quoted as vast influences by most of black metal musicians, but I don't think anyone would call them black metal.
creating a term =/= creating a genre/subgenre of music
Again, it depends. Meshuggah coined the term djent, which is a more or less decent umbrella term for their copycats, based on their specific riffing/rhythm qualities. It became a sort of style, based on particular musical elements that
can be traced back to their originators.
Now, I don't consider Venom to be a black metal band. They might have brought up the term, but they never made black metal. Even Hellhammer was closer to the black metal sound than what I personally consider to be established from Bathory's debut onwards.
heavy hardcore =/= metalcore
Sure. Heavy hardcore would be more like crust, not metalcore.