The "philosophical view" that "there's nothing out there" indeed does not disturb me; but I don't think I'm an exception. Despite some modern-day movements to respiritualize the world, the current diagnostic is that we live in a secular, cynical, nihilistic, indifferent, blasé, uncaring, hedonistic society. Lovecraft's and Ligotti's standpoint are, to a large extent, the mainstream opinion of the majority, even if they articulate it more through deeds than words. In that sense, both authors explore old-fashioned fears that I think mean nothing to the vast majority.
I can take a wider view and appreciate that in the 1930s it was shocking for theists, still coping with Darwin and the "death of God", to entertain the notion that there's no ultimate meaning foregrounded by a deity. But I take that for granted so I never felt any anxiety about the bleak, neutral, empty, silent universe; in fact I find it pretty liberating since it means I can imbue my life with my own meaning. That means that these bleak "philosophy" bores me as much as the awful French existentialist novelists that always seem to start with the premise, "I'm so miserable because God is death and now I have to take responsibility for my actions". Like duh, no sh*t Sherlock!
So I can appreciate it from an historical pov. But I'm not beholden to what authors believe; there's a big distance between knowing authorial intent and caring about it. That means the only thing worth taking away from Lovecraft, in my humble opinion, is the "silly entertainment" you seem to be so dismissive of. I just want to appreciate fiction aesthetically.