I'd say the opposite question would be easier to answer: "at what point does poor image quality become consequential, and ruin an otherwise good image?"
I can think if several examples from my digital P&S days, where I thought, "that's a nice picture, too bad about the blown hilights, digital noise, lens flare, etc."
^ This.
It's silly to ask "how much do I need," because that depends on so many things, personal standards included. There is *no way* someone else can answer for you as if there is some independent standard.
It's also silly to assert that "good" photographers can make "compelling images" with whatever no matter how crappy. I say it's silly because nobody says "That person is a really good photographer but all their images are boring and really just not compelling or even in focus or so much as developed properly."
Quite obviously, by the time one says "That's a compelling image," one has already gotten past medium and format and technical shortcomings. And it's only in the taking of "good" photos that we define "good" photographers. IOW, they don't get good images because they are a good shooter, we say they are a "good" photog because we like the images. We are free to discount images that are technically shoddy regardless of the content or the skill of the person behind the camera. We don't even acknowledge the skill until we like an image.
One might as well suggest that a print with dust and lint on the negative and stains, fingerprints, and creases on the paper is just as nice as one where the printer took obvious care with the entire process. At which point, why even care about your craft?
On the other hand, I think everyone has taken a shot that would be nice except for how it *actually* showed up on film or in the file.
I contend that one needs to be aware and work within the limits of their medium to achieve quality work. But that doesn't mean a person has to be content with inferior equipment or pretend there are not serious limitations with their chosen format. There is a point for everyone where they decide things are not up to their personal par. You won't take more interesting pictures with more expensive equipment, but you might get technically better images and be able to realize a creative goal that was out of reach using more limited tools.
My comment about 110 film speaks to this directly. If the equipment truly doesn't matter, then why *not* use 110? It appears I'm not alone in preferring a larger format and more control over the image-taking process. One might legitimately argue that "enough is never enough" but reality sets limits we must accept. And we all have our own limits and tastes. So one might chose 35mm, another digital 4/3, or 8x10, or whatever. Everyone makes their own valid choice given what is available to them. IMHO, if you are unhappy with what you are getting, try something else rather than accept it simply because it's good enough for other people.