No, SketchUp does support perspectivic texture transformation (4 texture pins freely placed) and internally keeps a single texture. But under some circumstances, namely export, it assumes the export format supports only affine texture transformation (3 texture pins freely placed, 4 texture pins always form a diamond). Then SketchUp makes textures on faces with perspectivic transformation unique.
- You could keep discipline and avoid perspectivic transformation altogether (use only red, green, blue texture pins, never touch the yellow one).
- The Collada exporter also does not support arbitrary texture transformation unless for “projected textures” (projected from another face). If you at most use texture projected from another face and export to Collada instead of fbx, you could also avoid the problem.
- You could use this conversion script that tweaks perspective distortion to become affine (depending on the mesh it has a more or less visible effect).
- You could also search for another exporter (extension, commercial extension, e.g. maybe the Simlab ones) that properly exports perspectivic texture transformation.
Maybe SketchUp 2020 should feature updated exporters that export perspectivic texture transformation without texture writer whereever the fileformat supports it (this can be a checkbox in export options).
In case of using texture writer, SketchUp 2020 could have the option (also in the API) to bake the texture shards all into a single texture atlas.