Stopping prisoners from harassing their victims/witnesses against them/enemies or organising others to do their dirty work externally is already a massive problem. Prisons have the ability to listen to calls and read mail to try and curtail it.
Giving them access to the internet makes all of this far easier, and monitoring it far more expensive. Not to mention that now they can use the internet to commit new crimes, and they have nothing better to do for the years or tens of years that they're sitting in a cell.
I think giving them access to email is do-able, since that is no different in practice to physical letters. But giving them unrestricted access is a monitoring nightmare.