It's strange reading this thread, because of the occasions I've known of in RL where a letter or conversation with the OW/OM actually helped the situation and promoted healing.
Where this has happened, the common denominators were: the third party giving no excuses - just a heartfelt apology for their part in causing the recipient pain; acknowledgement that the straying spouse loved the partner very much and didn't want the marriage to end; an offer to answer any questions truthfully if requested.
Recipients of these letters have said that this action divested the third party of their 'power' and allowed the morbid fascination with them to cease. Those who've taken the opportunity to ask questions were relieved to hear that their spouses were telling the truth after all about aspects of the affair and this enhanced trust.
As long as the motive behind it is selfless and is genuinely about relieving the faithful spouse's pain and uncertainty, I think it is a very good idea and can have positive results.
Generally speaking, the faithful spouse doesn't want to know anything about the third party's motivations for doing what they did; they are rightfully more concerned about why their own partners had an affair and whether they are telling the truth about what happened and what was said/promised.
Many people also say they can try to forgive their partners because they have received an apology and have seen the contrition first hand, but because they have received no such apology from the third party and don't know if s/he is sorry, the resentment and bitterness towards this person festers and stops them from healing.
It's true that the people who are most receptive to this type of communication are those who generally have good interpersonal relationships and don't like the fact that they feel lingering enmity towards another person and are self-aware enough to know that an obsession with the OW/OM (which is completely normal and understandable in these situations) is holding them back.