The only way to export animation in fbx format is to export baked animation. There is no options to export objects with animation keys that were set in exact frames in exact transformation channels. There is always some sort of interpolation accure with adding extra keys while baking animation. Simplification option removes necessary keys and there is no way to keep them. In game dev industry piplelines very often it is very important share models via fbx with original animation keys. Absence of this option is a huge drawback that prevents Blender from becoming an industry standard. By the way, the option to export animation with out baking implemented in 3ds max and Maya and works well. Therer is no blender addons with propper export options.
Blender FBX exporter needs improvement.
I made some sort of Blender → 3ds Max bridge that consists of two scripts, first is blender addon to store in JSON file such data as euler rotation order, objects hierarchy, raw exact rotation and location animation keys and objects collections names, and second is 3ds max script that restore all data from JSON file to the same clean objects that were exported/imported to 3ds max via standart blender fbx exporter. The end result of these manipulations is the scene made in blender but automaticly reassembled in 3ds max. With this somersault it is possible to use 3ds max exporter to export all objects with exact animation keys as they were made in blender. I hope blender developers will someday turn their attention to improving blender fbx exporter, but until then it can be useful for sertain number of 3d artist to use this not very simple method.
Github link