They are differentiable which allows for image based rendering via solving the inverse of the rendering function via gradient decent

I'm not an expert and have not yet worked with splats, however I understood that unlike super-sharp-edged triangles they can represent complicatedly-transparent 'soft' phenomena like fur or clouds or similar that would ordinarily need to be rendered using possibly semi-transparent curves/sheathes (for fur/grass) or voxels for cloudy things like steam/mist. I gather splats can also represent and reproduce a limited amount of view-dependent specularity, as other commenters have said this is not dynamic and cannot easily deal with changing scene geometry or light sources.. still sounds like a fun research-project I make it do more in terms of illumination though!

It's really not a splat vs triangle thing. You're basically comparing points cloud data to triangles.

Likely triangles are used to render the image in a traditional pipeline.

It's just a simpler primitive I assume. Blurs and colors and angles are simpler than 3D geometries, so it's probably more aligned with working/thinking with other very low-level primitives with minimal dimensions (like the math of neural networks). I dunno, I'm kinda vibing a response here -- maybe someone else can give you a more authoritative answer