Is this because there is no proper C4D pipeline like Maya, Blender, UE, Unity and 3DS?
I can’t comment on the game engines or 3Ds but I have Maya and Blender
the Maya “pipeline" from accurig is just vanilla FBX export but Reallusion does provide a
Maya HumanIK rigging profile to convert your Character Maya HIK then Maya's animation tools do the work of retargeting my actorcore motions.
For Blender there is a separate Pipeline addon ,created by a single user, to import FBX from Accurig
convert the characters rigging to Blender native control rig & retarget actor core motions ,including facial animation from CC3/4.)
But there are also non reallusion addons to retarget actorcore motions to the Blender rigify
control rig as well.
Maxon C4D does not have a useful NATIVE general purpose retargeting system other than that old one that only works with Mixamo rigged Characters.
The video ,linked by PeterRL, is by a very promising Actorcore retargeting solution
with a Control rig ,created by a private individual, which is likely to be your best option ,(if its development continues) other than applying the actor core motions in iclone and importing the character from CC4 already animated for rendering.