The thing about Venom and the symbiotes is that they are by far the most popular villians Spider-Man ever faced, bar none.
I think it all ties in to the very personal motives driving Eddie and the suit; they want to beat on Spidey and nothing more. Nothing about money, power, fame, or whatnot. They just want to take Spidey, rip out his spine, flay the flesh from his bones, and feed homeless people with his remains.
While Doc Ock, Green Goblin, Electro, etc. all have history with Spider-Man, none of them were ever nearly popular as Venom is.