> Seems great to allow it through monitored devices for free, you might gather more evidence this way and convict others.
The conviction already happened. Continuing to gathering evidence (for any purpose other than exoneration in cases of suspected wrongful convictions) - and without new warrants - violates the spirit of double jeopardy (Fifth Amendment).
> Obviously the right to privacy (4th amendment) is lost in prison among other rights so there shouldn't be any issue with the surveillance.
When you say "Obviously" do you mean what things are like, or do you mean what things should be like? If you mean the latter only, then I would agree with you. (Although, I'm not sure whether the US constitution implicitly supports a right to privacy.) The chilling effect means that both the convict and the loved one on the other end can't freely express themselves in a private conversation with each other. If your family member gets prison for life then should you lose your First Amendment rights whenever you want to talk with the convicted family member? By default, criminals shouldn't have zero speech rights and zero privacy either. Whether someone is dangerous or has done immoral things is on its own not enough reason to take away constitutional rights. One possible reading of the 13th Amendment allows slavery and involuntary servitude "as a punishment for crime whereof the party shall have been duly convicted" [1], but the same doesn't apply to other rights.
In the context of prison, freedom of expression and privacy are about as important to me as voting, and I'm not a fan of felony disenfranchisement [1]. In my opinion, US citizens in prison shouldn't lose their voting rights for any period of time, especially considering that vote by mail exists.
[1] https://en.wikipedia.org/wiki/Thirteenth_Amendment_to_the_Un...
[2] https://en.wikipedia.org/wiki/Felony_disenfranchisement_in_t...