Humans are the only species, the claim goes, aware of the fact they are going to die one day.

So maybe thinking of it is just symptom of condition called "being human".

Also, not all cultures have the "zomg, death is horrible, don't talk about it, don't think about it, pretend it's not there" attitude. I read many philosophical ponderings about today's funerals, and how they are impersonal and fast and preferably hidden from sight (not many funeral processions anymore)... and none of them saw it as "good".

I'd be vary of person who honestly never thinks of death.