To be fair, that sounds like a fun concept. However, one doesn’t need a powerful homebrew solution in order to get such a character unless you only care about a direct translation of the mechanics over the flavor. I’d personally either go Dragonborn Undead Warlock or Dhampir Draconic Sorcerer for such a concept personally. If neither race is available, then I’d play a human or elf caster with access to spells that can help mimic abilities that dragons and vampires have.
As far as the greater topic is concerned, I have to agree with the greater majority on this thread that I don’t see a problem with DMs having restrictions for their campaigns. I would only ask to know those sorts of thing up front, which most of the DMs posting here have already stated they do. I’m much more worried about the overall theme, playstyle expects, and plot of any given campaign then I am about whether every single PC option is available or not.
I of course do have my preferences. I love playing monstrous races like Yuan-Ti, Kobolds, Kenku, Thri-Kreen, and the like. However, if these were not available then I would make the concepts I want to play work with the race options available, and it even gives me a chance to be creative with them.