So interestingly, one distinguishing difference between oil paintings and acrylic paintings is that the former has more translucency, whereas the latter can be more easily layered on in a way that covers up the lower layers. This is what, according to one of my mentors in art school who was a painter, allows oil paintings to copy the feeling of real skin so well: it allows a painter who mastered the medium to create a similar subsurface scattering effect. That's also another reason why paintings in real life can look so different than images on a screen, aside from the much greater gamut than even the best color screens we have and the actual surface texture of the paint strokes. The downside is that any mistakes made on deeper layers will come through in higher layers. Especially if you paint using the techniques used by the old masters.
Anyway, this suggests your gaussian splats essentially are closer to "oil painting"-like. Makes me wonder if you could also encode this subsurface scattering and texture somehow, so that viewing the splats in 3D would recreate some of that missing effect of looking at a real painting!
Also, on the other end of the spectrum: do you think the algorithm could be modified to create SVG output? Then it might be useful as an artistic "upscaling" filter too.
(Also, speaking as someone with protanomaly, I'm guessing the links have some kind of turquise or light teal color to them, but it is effectively bright gray to me. And since they have almost the same brightness perception as the white text I genuinely cannot tell where the links are (except when the text calls them out). Since this is likely to affect anywhere between 5% to 10% of all men visiting your blog that might be worth changing.)