It doesn't really do anything for me as a style in it's own right. To be honest, lazy hipster nostalgia bait is exactly what it looks like and little more.
I totally get where you're getting at with the comparison to things like impressionism. I feel similarly about older 3D stuff like the original System Shock or PS1 era low-poly 3D. There's a certain kind of openness, and, paradoxically, realism that I find in these old 3D games that I don't get in modern 3D stuff.
However I don't attribute that to the low res construction in itself. I think it's more a case of low res forcing a certain approach to environmental design, combined with unintentional visual side effects of the low poly/low res stuff to create a certain general impression or atmosphere.
I think modern games tend towards the visually over-designed: they try to maintain a certain high minimum level of detail density everywhere, and as a result there's types of interesting/cool composition you just never see. Everything has to be crowded and structured. Every surface and volume has to work hard to justify it's existence, or else be culled to make overhead room for more detail elsewhere. No space can be spared for visual pacing, as were. A long blank wall can't be plain, even if that would suit the composition best, because that much plain area is "wasted real estate" in the developers mind, and has to be broken or gunked up, and if it can't be broken or gunked up, that part of the map gets shrunk or cut to eliminate that real estate. I feel like this aggressive minmaxing for uniform detail density is actually part of why some franchises become more linear and boxed-in with each sequel. The devs think they're improving the level design by trimming fat here to add detail there, but they're actually making things increasingly compact and homogeneous 'till everything starts to feel fake and claustrophobic.
I think that same vibes I get from older 3D titles can be achieved with modern technology at modern resolutions, and I think the same is true of the impressionistic quality you attribute to pixel art. The art is in the feel of it, the way it communicates. The technical method is just carrier media for those things, not the art itself, whether it's brush strokes or pinch-blobs of clay or pixels or polygons or whatever. This is true of all art styles IMO (well, except for some weird stuff like mathcore music, but even there the notes are more the point than the instrument), but especially of impressionism in particular. The whole point of impressionism was to make images dithered out of abstractions, the way you see things in a dream or a memory. If you're focusing on the technical paintstokes, you're putting the cart before the horse at best.
IMO the better comparison would be pointillism. Pointillism is strongly associated with impressionism, but it's not the purpose of impressionism, nor is it essential to the function of impressionism. It's just the brush technique pioneered by impressionism. Pixel art is a kind of ultra-restrictive digital pointillism.
I'm also not really a believer in art shaped by limitations as an ideal. While great works have been shaped by limitations, I feel that seeking out limitations would say more about the artist than the value of said limitations. Relying on limitations to improve one's art seems a crutch at worst, a training exercise at best. A really good artist would be able to create the same feelings with the same impressionistic aspect as pixel art using unlimited/freeform tools, and to me that's what makes pixels just look like redundant outdated tech instead of a style. I feel like the only non-redundant thing it brings to the table is the purely technical aspect of being little squares. There's nothing it can do that can't be done with a regular paint program.
Now, use pixel art as pop art instead of impressionism, and you might be onto something. But then pop art is basically a hipster irony Inception loop of the high-art world smirking at itself in the mirror, so while it might make more sense, it might not make it better.
Mind you I'm specifically talking pixel art here, not sprite-based gameplay, or low-tech indie games. I can totally understand some indie games needing to go low-tech, but no one needs to go as far as pixel art anymore. Modern systems have zero trouble with high res sprites, and low poly 3D animations are if anything just as easy or easier to make these days (one of my favorite indie games of the past couple years is Shadowrun Returns, which is tiny low-poly 3D toons on painted isometric backgrounds) so pixel art is obviously being done for it's own sake, not for technical reasons.
In extreme cases it works. I love FTL, and I think the pixel art works fine there because it's SO simplified that it's almost a total abstraction, like a chess board. At higher resolutions is still looks more fake-retro than arty though, so I wouldn't mind having higher res assets for larger monitors, and the bigger you go, the less justified the pixel art feels even for an abstract style. As is it's the world's most perfect mobile game, though.
