Can it? Definitely. Should it? Yes. I think it is the essence of thinking of death in general, considering even your own demise has - for me - a sense of awakening, finding that bit of you that has become complacent and slapping it awake.

Aknowledging their death through introspection and finding yourself lacking might also hint at the value placed on the life lost, I think anythink that makes you pause to consider such questions surely has to have value as we don't pause to consider these things when listening to the horrible stories on the news, instead we lash out.

Something that makes you look critically at yourself is connection and when you lose a connection you need to evaluate and re-establish what was lost. This does not take away but instead does the least and the most you can possibly do. Acknowledge.

Sorry for your loss and apologies if my response seems apathetic.