What is Poe suggesting about the limits of human power to escape death and fate?
Ultimately, Poe suggests that humans -- no matter their identity or circumstances -- do not have the power to escape death. As mortals, we are unable to avoid death, our natural human fate, forever. Death will always, eventually, come for us all.
The prince has a lot of money, but it doesn't matter; his money cannot save him. The prince has an isolated abbey where he can hide away with all his friends; it cannot save him. He has the power and ability to remove himself from the location where the Red Death is decimating the country's population, to surround himself with only happy and healthy friends who bring no risk of disease; these cannot save him either. He surrounds himself with imaginative fancies, grotesque dreams of feverish imaginations designed to distract himself and everyone else from their mortality, but that's all these dreams can ever be: a distraction only (and even then, they are imperfect because people continue to be reminded of their mortality every time the clock chimes). They do not and cannot actually shield him from death, as the Red Death makes very clear.