If the A340 could not make the route economical, then that suggests that my argument is indeed valid. If in the future they find that demand is picking up to larger levels, then there would truly be a case for asking why LH pilots are not flying it.
As I can see though, it is still a new niche service.
Bear in mind that PrivatAir do not operate anything larger that a 757, and they only have one of those, and there is unlikely to be much freight that can be placed on the BBJ extra to the pax and their kit due to the extra tanks.