It all depends on WHAT kind of vampires we're talking about. After all, there are also ghouls, sort of poorly made vampires who really just need blood and flesh. Otherwise, I agree with you.
As for the sword, it doesn't hinder them at all, as has already been said here. I'll tell you about such vampires, they're called Nosferatu, who don't need to "latch" onto the victim's throat. It's enough to simply slightly cut the client and, using dark vampiric magic, suck the blood directly from the wound at a distance, which, by the way, is quite vividly depicted in the game BloodOmen2. After everything I've said, here's the question: Why do vampires in Heroes 5 need swords?;)

NOSFERATU. Deformed, bald, terribly hideous vampires. They always
stay in the shadows and live in sewers. These are spy vampires, agile and
cunning, they are difficult to detect. They are ruthless, but still emotional.