Well, it all depends what you consider "bad".
Many of the reasons that a person would end up in prison, such as murder, assualt, rape, pedophilia, armed robbery, etc. are "bad" as far as I am concerned, regardless of one's childhood, thousands of people have had horrible childhoods and do not go on to be criminals.
Don't forget too, while in prison, some of these pen pals of yours, may be telling you "nice" things that may be untrue for your sympathy, sure they are lonely but they have only themselves to blame for being there.
I do understand this is not always a black and white situation, lot of grey area, so I can understand some benefits for the prisoners and even the writer.
I can understand more though, how writing to people in psych wards or re-hab can benefit those, and also those away from home in the military, these people get lonely as well.
I hope whoever does correspond to those in prison do not fill them up with false hopes, etc. but just some light conversation, to help prevent triggering any unwanted behaviour.
I'm sorry I don't fully agree with you on this, but if you like writing to them, it's your right to do so.
Please take care and be careful,

DE