In some shows, Vulture is Spidey's first villain to face. Also, he's lower tier than most others. That means that Spider-Man can grow better to face stronger villains in time. This'll allow not just more characterization(and for Vulture too, as his backstory is simply a little better than just "I wanted to be evil" or "I made a mistake and injected myself", but actually was screwed over by someone badly and wanted to get back at them. Well, depending the storyline. This could be interesting. The first set of live action films actually made some villains more tragic, and it also made them more interesting in return). I think this means he won't be generic, but also will be enough of a challenge for Spidey to grow as a character in general.
Plus, when doing a reboot, you should never start with super powerful villains. Green Goblin is one of Spidey's most powerful foes. He's almost always enhanced like Spider-Man was, and full of major artillery that can clearly kill people, as the live action movies proved. In addition, he's not always tragic either. Depending if it's Norman or his son. For his son, he usually is part of a tragic story. But Norman has rarely been show as anything but a jerk at best. Now, Green Goblin could be hinted at or show up later, maybe, with his son taking the mantle or playing a role in the story. Harry is interesting like that.
Also, you do realize that Venom is one of the few Tier 1 villains that Spidey cannot beat outside of using something besides his basic talents. Kraven he can trick, or use his agility. Lizard too. Venom most often won't activate the Spidey sense, which already forces Spider-Man to be on alert and will likely take a pounding. Yes, Venom has a major weakness in sound, but in many cases, killing the symbiote can be next to impossible. Especially as the MCU under Disney(Hulk and the Agents of S.M.A.S.H. has Doc Ock use Spidey's own blood) shows that Spider-Man's blood can potentially create another Venom if he was infused with it. Even in older shows, I doubt that Spidey had zero Venom cells in him even after discarding the symbiote. More like dormant and unused cells. DNA doesn't magically change after being infected. Plus, there was never an antidote, just sound removing Venom from keeping control. Technically speaking, there's nothing to suggest Spider-Man lost every possible cell that had the symbiote in it.