Short answer: You can do and write whatever you want. You can make almost anything work.
Long answer: Death is an idea, the belief that there is more to a human than flesh and blood, and that when we die, something mythical happens. Casting this idea into a character allows others to interact with this character, and also allows the writer to make comments on the image people have about death. The same thing can be done with any idea, and it used to be common practice to think about ideas as persons. The roman and greek gods are probably the most prominant example, but most polytheistic religions follow this idea to some extent.
This also leads to some prime examples about good stories with interactions between characters like this, Homers Ilias are probably the best known example of mortal characters interacting with idea-based characters, although these incorporate a lot of additional lore that progresses the characters.
Incorporating an idea into a character allows interactions that are otherwise not possible, it allows the sea to be explicitly angry at a character, it allows a character to chase the magic fairy that grants eternal youth or be hunted by the demon that will stop you from being reborn in the reincarnation-cycle.
So yeah, characters like death can be good and interesting. However you might have problems expanding the character from the original traits that define it, thus making your characters slightly stale. So if you do, make sure to expand their backstory.