I would be interested in you perspective on this: http://arstechnica.com/tech-It must be understood that high phone fees at prisons are an ongoing situation within the current statist system. It has nothing to do with libertarianism.
policy/2015/10/prison-phone- companies-fight-for-right-to- charge-inmates-14-a-minute/
In addition, you have the problem of the current criminal system, itself, which would be far different in a libertarian world. This includes large sectors of the current prison population, such as drug dealers, who wouldn't even be considered criminals in a libertarian society.
I suspect the high phone fees are simply part of the crony statist system. It is an easy way for those in cahoots with government officials to make money against the relatively weak. Prisoners are an easy target to abuse. Who wants to spend time fighting for lower phone bills for "criminals"?
Don't get trapped into thinking that there is a libertarian answer for high phone bills versus low phone bills for prisoners. It's a statist trap.
As far as the phone companies being "private" that is another trap. The word "privatization" has two very different meanings. There is privatization which means getting the government out of a sector, where the government doesn't even set the rules in the sector. That is libertarian-privatization. Then there is "privatization" where the government continues to set the rules in a sector and hires outside contractors instead of using government employees, This is just a government shell game, where it remains a government controlled structure with the payees being changed only in legal structure from government employees to government contractors and employees of government contractors.
True justice from a libertarian perspective would not be focused on the cost of phone charges, It would be on opening the gates of the prisons and letting everyone out and throwing the exces of the prison phone companies, the execs of "privatized" prisons and the crony government officials, in the cells.
If someone has claims against a released prisoner, because of violations of the nonaggression principle, then those should be dealt with in libertarian court systems after they are released.