We're as much a part of the planet as its rocks, and we care. You could say that your bones don't care, but the organism that is you cares. In the same way the planet cares through the subsystem that includes us even if its rocks don't care.

You're right if you define a planet as its rocks, and would also be right to assert that humans don't care if you defined a human as its skeleton.

If room temp superconductivity leads to a practical fusion reactor, a good portion of earth destruction for energy development will end. Starting to fix things first involves stopping the destruction of things.

Norm Macdonald responding to Neil Degrasse Tyson on twitter.

Neil: The Universe is blind to our sorrows and indifferent to our pains. Have a nice day!

Norm: Neil, there is a logic flaw in your little aphorism that seems quite telling. Since you and I are part of the Universe, then we would also be indifferent and uncaring. Perhaps you forgot, Neil, that we are not superior to the Universe but merely a fraction of it. Nice day, indeed

In the long run, life on Earth would expand from the extra CO2 in the atmosphere. Pre-human CO2 levels were on a long downward trend, likely just a few million years from dropping too low for photosynthesis.