When I picture good uses of pixel art in modern (not retro-aesthetic) games, I picture it not as a pixel “camera” — a low-res CCD capturing a grid of samples of an originally-high-fidelity world; but rather as the world itself being made up of a bunch of vector squares — like the 2D equivalent of a Minecraft voxel world. The camera is a regular high-resolution camera, looking at a weird blocky world.
In such a world, rotating a pixel sprite by 45 degrees should just look like there being multiple invisible “grids” to the world, each rendered at infinite resolution and downsampled to your display, where the sprite isn’t rotating per se, but rather the pixel grid “layer” the sprite is on (i.e. the hi-res texture the sprite layer is being rendered onto for compositing) is itself rotating.
Of course, if you’re going to use things like rotation/scaling, sub-pixel particle effects, 3D, etc. then you then either have to embrace it in your game setting’s art design everywhere so particular uses of it don’t stick out; or you have to acknowledge that any uses of it are basically “non-Euclidean geometry” from the viewpoint of in-setting observers, and thus slide your game’s mood toward something approaching either science-fantasy (e.g. Fez) or horror (has anyone done a Flatland Cthulhu game yet?)
Also note that “multiple distinct pixel grids” isn’t even unprecedented in retro games, either; there were plenty of consoles where you got one resolution for your tile map and a different (usually higher) resolution for your sprites; where sprites could sit on top of tiles in non-aligned positions. A few consoles and arcade cabinets even combined pixels with vectors!