It likely is somewhat profitable, but would require a huge investment. Some have suggested (can't find the source) that the DSN should be charging closer to $35,000/hr to cover costs of maintenance and building new dishes to expand the network, but NASA themselves can't be a for profit company. So if there was someone providing commercial ground services for deep space, lets say with commercial efficiency they get services to cost $20,000/hr. Great! But why would I do that if I can still go to DSN and pay $5000.
But as the article indicates there were probably be a reckoning soon because I've already heard people describe scheduling and allocation of DSN time at JPL as a battle royale.
https://deepspace.jpl.nasa.gov/files/6_NASA_MOCS_2014_10_01_...
That also explains the challenge for private investment. If none of the missions are budgeted to buy bandwidth, then you would have no customers for a private DSN service.
Could this be commercialized? If there's high demand it should be profitable to build new dishes to increase bandwidth.