No the original story with Vulture never even included the Symbiote. The problem wasn't the amount of villains, it was how each were treated and fleshed out as a character in the movie's screentime.
Vulture:
*Wants revenge on Spidey for an illegal bust (something that may or may not have even been shown in the movie). Now he lost his business and is forced to spend what little life he has left in prison.
*Toomes (who wants revenge from the start) would have spent a substantial time in prison before Sandman breaks him out, leaving more screentime for Sandman, Harry, etc...
*Plus the team up would have made sense, cuz him and Sandman were cellmates.
Venom:
*Introduce the Symbiote
*Introduce Brock and Gwen Stacy
*Show the rivalry between Peter & Brock and give reason for Brock to hate Peter/Spidey.
*Show Spidey with the symbiote and its effects on him and the people around him
*Spidey looses it, then the symbiote goes on to Brock creating Venom.
* Venom teams up with Sandman for the finale.
Now are you honestly going to say that with Vulture, it would still been way too much?