Exodus miss out on this criteria because they did not sell as many records or become as popular. But some revisionist types believe they should be included in a revised "Big Five." This partially makes sense, because Exodus were around from the beginning and helped pioneer the sub-genre. So their influence, maybe, cannot be understated.
OTOH, Exodus were just not as consistent song-wise (or album-wise) as the bands in the Big Four. This works against the band's favor, because they dabbled in mediocrity. Therefore their influence, however important it once was, is mostly forgotten as a result.
History is told by the winner, and this argument irrelevant. Who knows. But it is fun to talk about!
Gary Holt is a tremendous guitarist, and the band had a lot of brutal power in their sound. But Paul Baloff's vocals were atrocious, and singer Steve Souza, while better, was nasally. Influence is one thing. The fit to become a star (and go down in history) is something else.
NP: Flotsam and Jetsam - Are You Willing