That is, do you feel that objects have some sort of objective measure of coolness which is worthwhile to preserve even in the absence of any subjective viewpoints to make coolness evaluations?
Do you care intrinsically about anything which isn't a mind? This seems to be something that would vary individually.
It's an interesting question; so far, the closest I have to an answer is that any timeline which doesn't have minds within it to do any caring, seems to be to not be worth caring about. Which leads to the answer to your question of 'nope'.
Thought experiment:
Through whatever accident of history underlies these philosophical dilemmas, you are faced with a choice between two, and only two, mutually exclusive options:
* Choose A, and all life and sapience in the solar system (and presumably the universe), save for a sapient paperclipping AI, dies.
* Choose B, and all life and sapience in the solar system, including the paperclipping AI, dies.
Phrased another way: does the existence of any intelligence at all, even a paperclipper, have even the smallest amount of utility above no intelligence at all?
If anyone responds positively, subsequent questions would be which would be preferred, a paperclipper or a single bacteria; a paperclipper or a self-sustaining population of trilobites and their supporting ecology; a paperclipper or a self-sustaining population of australopithecines; and so forth, until the equivalent value is determined.