You just do no understand how it works. All programs have own file format and they forbidden to using in other software because of copyrights. So we should using third party file formats what opens to exchange FBX or OBJ but because progress moving, every day new technology exchange formats cannot be often updated, actually autodesk trying update FBX and it have versions 2018.2019.2020 etc and this is issue compatibility for other programs. So this exchange format have more compatibly but only have few features to store texture like color, specular, opacity etc but it cannot store PBR materials (roughness, ior etc this is new physical base shader what most modern software using including viewport of 3dcoat when you drawing texture) even pbr have own standard for specular channel, also normal map for many program a bit different. So in another program you have to make your own shader and collect textures manually, insert in right slot, invert normal map\set gamma(remember i said they are different)
It's all because FBX and OBJ cannot store modern PBR workflow as they are old third party file format for exchange only between 3d software and mostly only for 3d mesh not for materials. There is substance painter from Adobe now what have own sbsar format and some program including unreal engine may import with ALL settings in shader but this may lead to another problems.
3dcoat yes a bit not intuitive, but if you look in similar software like zbrush and substance painter they are even worse and more complicate. Did you saw photoshop and illustrator? They are look the same but many similar features work completely different way this is blow my mind when i saw how works applying gradient to text in both softwares or how they work with vector compare to Corel draw for example. And because photoshop have huge base, template, mock-up stores etc, we cannot throw it away, that's why own format is bad.
To conclude my text you need just to study how to make shader in final program, this is not 3dcoat related if we talking about textures, you may see material library like quixel megascan (it is free by the way) mostly they are provided just this textures even if you have option to import in final program they are often wrong and you need to adjust settings in shader manually