Once they have D2 flying regularly I suspect there will be some private missions. The lunar flyby was a a pretty special case. It's an opportunity to buy a place in history and get lots of global publicity. The second and third time not so much. Once SpaceX passenger launches to the ISS are common, there won't be so much attention paid to private astronauts in LEO.



I think SpaceX did try to stir up interest from foreign governments and private citizens without getting many deposits. They had a similar experience with F1 that lots of people said it was a great idea until it came time to sign contracts and write checks then things got a lot quieter.