People have been coping for so long it's practically a genre in literature. People are convincing themselves so hard that immortality is a curse, yet literally zero people have actually experienced it.
"The only problem about being immortal is that you need to drink blood, a set of ethical problems spanning a tetralogy", so I haven't really seen/read about the exact idea you're talking about. Got any media where people actually say your kind of Immortality is bad?