That’s not correct. You can bake filmic, but some of the blender/cycles colorspace assumptions make it not immediately obvious.
First problem is the target texture: If it’s 8 bit, blender will assume it’s sRGB and will ignore your CM settings. I.e.: it will clip anything above 1 and encode to sRGB curve.
What you want in this case is to keep the rendered scene data and apply the filmic transform, so sRGB won’t cut it.
The way to work around this is to create a new 32 bit texture as the target for your bake, which will result in a properly scene-referred image, and then you have two options: You can either save it as EXR and keep the scene values, or “bake” filmic and save the result as an 8bit texture.
For the latter, that ludicrous* checkbox “Save as render” will do the job, provided you set your CM to filmic already.
*) It does exactly the opposite it advertises: It saves not the data as rendered but the data after the view transform.