I can see cozy SFF working out in a larger hellscape in one way, and in a way that may be more relevant and hopeful than things generally being fine (which to many today may seem the biggest fantasy of all): Things generally aren't fine and there's not much we can do about it, but we can build meaningful connections and alternatives in this sphere where we have some control, and--crucially--rather than hide away from the horribleness, we do what we can, sharing resources and wisdom, spreading a little hope, figuring out how to treat each other well and make reciprocal community work out in a world built on violence and exploitation.
In a way this is even more subversive a story than hero-saves-the-world high-stakes SFF, because it subverts the idea of individual hero-saviors (who in my mind are just villain-tyrants in waiting--live long enough to see yourself become the villain, etc.) altogether, not to mention the idea that we are just a few villain deaths away from utopia. With a focus on community it's possible to say instead that our problems are systematic and institutional in nature and we can't kill our way out of them, nor will a small band of Great Men come riding in to save us. Rather the work of world-making, remaking and building it every single day, lies with all of us and how we learn to live and work together. In this sense cozy SFF, and cozy stories in general, have potential as a very anarchist kind of storytelling, too.
Re: Just by way of background to your points
In a way this is even more subversive a story than hero-saves-the-world high-stakes SFF, because it subverts the idea of individual hero-saviors (who in my mind are just villain-tyrants in waiting--live long enough to see yourself become the villain, etc.) altogether, not to mention the idea that we are just a few villain deaths away from utopia. With a focus on community it's possible to say instead that our problems are systematic and institutional in nature and we can't kill our way out of them, nor will a small band of Great Men come riding in to save us. Rather the work of world-making, remaking and building it every single day, lies with all of us and how we learn to live and work together. In this sense cozy SFF, and cozy stories in general, have potential as a very anarchist kind of storytelling, too.