Maxperson
Morkus from Orkus
The rules don't say anything about blood drain. In fact, we know that in this scenario the PC died because they had their max HP lowered by wights. Wights don't drain blood.
Vampires do piercing and necrotic damage. They may do that by sucking blood but as far as the rules are concerned there is no mention of irrevocable blood loss.
The blood portion was pretty irrelevant, though, which I mentioned in a prior post. The max hit points hitting zero and dying is the important part. Whether from a wight or from a vampire, the effect is the effect. That said, the OP is very clear that it was death by Vampire. No wight was mentioned.
As for raise dead not working, I disagree with that as well. There is a clause in raise dead that if vital bits like your head are missing the spell doesn't work. There's no clause for not being able to regain a hit point.
I agree that it works. Then, because the hit point maximum is 0 and death happens at zero due to the vampire bite, the PC immediately dies again.