(I'm skating at the limits of my knowledge here, so corrections welcome if I'm in error!) AFAIK the advantage of triangles is that they are always flat - the three vertices will create a plane, so the polygon is called planar. A polygon with 4 or more vertices can be non-planar if one of the vertices is not on the same plane as the others. Render engines triangulate geometry when they render so all quads and ngons are split into triangles, but a non-planar polygon can potentially be split in different directions. The render engine won't split that poly the same way each time it renders, so that can result in unpredictable shading artefacts and flickering in animations.

As already said though, the modelling process is much easier with quad meshes. Selections are easier, edge flow for deformations is simpler to create and manage, subD is more predictable etc etc.

I can make one specific use case for triangulated meshes in Poser though. As Superfly doesn't have micropoly displacement I have made static props using decimation in Zbrush which results in pretty scrappy triangulated meshes, but I aim for a polygon count that keeps a lot of silhouette detail. I fix any major errors, make sure it works with a level of subD, and use the texture maps to carry the fine detail. Using more geometry does take more memory when rendering, but then so does using 16 or 32 bit texture maps for micropoly displacement, so it's a trade-off that I think works for some uses.

Base mesh, Zbrush screenshot, 50k triangles -

Final render, Superfly -

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