Those aren’t good reasons to disallow it. It’s already possible to bake static lighting to a moving objects using Light as if Static, just not skinned moving objects.
When you’re not aiming for photo-realism, or targeting lower-end hardware, it’s commonplace for character artists to bake or paint “static lighting” into their diffuse maps.
There’s a clear need for it here. OP could try to recreate his scene’s lighting and bake his own light maps in Vray or something, but that’s a huge amount of work to get around a problem that doesn’t really need to exist.