Modern writing based on the Lovecraft "mythos" forever oscillates between imitation and rote subversion. There is something in Lovecraft's writing that fascinates, and compels people to write more, but the results are pretty lackluster. The stories in A Mountain Walked - and I think nearly all mythos stories - end up being one of three things: Re-hashes of existing Lovecraft stories with the details changed, attempts at combining Lovecraftian tropes with other genres or moods that fall flat, and horror stories that have had some Lovecraftian terms pasted on, adding nothing.
Lovecraft's racism, his deep xenophobia, is inescapable. He situates the terrifying and incomprehensible in foreign cultures - "swarthy Kurds", "half-breeds", "islanders". A popular way to write yet another mythos story is to flip through the big atlas of world cultures and pick another native culture to insult in that fashion. In the compilation, Where Yidhra Walks, though well-written, is a prime example of this method, essentially porting The Shadow Over Innsmouth to a Native American setting.
This sort of thing is entertaining, but it leads exactly nowhere. It's a nice setting for a Call of Cthulhu campaign, but it neither interrogates or meaningfully builds upon the source material.
I believe there are two interesting things you can do based on Lovecraft's writing. You can confront and process the xenophobia of the original works, as The Litany of Earth does. I would especially love to see a mythos story written by someone from an Arabic background. That's where Lovecraft situated the wellspring of insanity-causing Otherness. The reasonable reaction as an Arab is to roll your eyes and dismiss the whole thing, but maybe an interesting angle to write from can be found.
The other thing you can do is very carefully separate out the "high Lovecraftian" idea of a non-anthropocentric universe, of human frailty, of the inadequacy of human senses and reasoning.
As it happens, a century of scientific research has given us a much more detailed understanding of such inaedequacies. Humans are consistently bad at understanding probabilities, we insist on seeing narratives and connections where there are none, we make decisions subconsciously and then create "logical" reasons for them, we are a mess of prejudices and blind spots. We build our self-identities on dangerously outdated information and yet can be incredibly suggestible under the right circumstances.
There are a number of mental conditions that positively scream to be used in a Lovecraftian story. Phantom limb syndrome. Blindsight. Face-blindness. Capgras syndrome. The accidental creation of false memories. I don't mean to suggest that you should write tired stories about "crazy" people, but rather that all of these conditions reveal just how fragile, limited and arbitrary our perception and understanding of the world really is.
Lovecraft was right, kind of: our minds and perceptions are indeed unfit to truly process the world, and we live in a series of convenient illusions that allow us to function. This is a fertile insight for fiction, and I would like to see more of it.