A possibility but again there would be a need to get away from the traditional tropes. The problem then arises as to what it is exactly though what you want to say/express about them. Personally I think a more interesting avenue of exploration would be the idea of the vampire travelling through time. Say take a single vampire created eons ago and then follow their story through history and explore the idea of what it means to be both immortal but at the same time incredibly vulnerable. How do you survive for countless centuries undetected and more importantly why? What's the motivation?
What you propose has also been done, interview with a vampire? or any of Rice's books for that matter.
And what you mention as a problem with the tropes is exactly why going back to Stoker's book would be ideal, while it certainly was the work that put vampires on the map, modern vampires are as removed from the ones of the book as it possibly can be. I really wish something like what Lucy becomes as a vampire to be brought to cinema, I've seen no vampire like that, vampires that lure children? that do not kill at once? ethereal and ghost like? all the things vampires can do and the things they are restricted by are so varied and interesting in the book, most people would think it's only stakes, wolves or transforming into a bat, which are actually pretty minor things with Stoker's vampires. Coppola's film just gave us a glimpse into all the convoluted rules they have.