Abandon widespread* texture use, return to polygons+vertex colors+in-engine cutscenes (and similar data-saving techniques like soundfonts).
my examples (2D: created with Godot, 3D: created with Blender)
spoiler Animated eye
This was using a feature that likely isn't viable (for common use) due to performance.
:::
And for something not-by-me, see Spyro's vertex color skyboxes.
* general normal maps are ok, but I didn't have much luck beyond using generated noise for metal. I even tried some stuff with watercolor, maybe with better shaders it could work but untextured is easier.
Or another example, any material you can just apply without alteration (for instance, make something look like wood) is alright too. Maybe UV mapping is not too bad, but extra per-model work is not ideal.