I think people tend to believe that "knowing is power", so the person (their cheating spouse/partner in this instance) has, supposedly, the "upper hand" as they possess knowledge the BS doesn't have. But in reality, in the case of EMAs, I do believe that having knowledge of dirty details you can never unknow about your spouse (even if you choose to split up, if there are children involved, this will certainly provide years of resentment with every forced interaction). I initally made the mistake of giving my husband some information when he barraged me with questions, but quickly realized that the more he found out, the angrier and unglier he got, so I flat out lied or withheld information.
I also believe that NOTHING good can come out of "coming clean", and like BR, I've also inadvertently lurked BS sites (with the intent of finding support) where it's proclaimed that "the truth and nothing but the truth" is the way to go, supposedly because "otherwise you're living a lie". Well, if that's the reason behind deciding to shatter your "chosen one's" world, then the WHOLE truth should come out (and it rarely does), which is more or less that you found your marriage so unbearable for one reason or another, that you had to seek joy and fulfillment elsewhere. But instead, he MM/MW is framed entirely in a light of "betrayer" and the BS as "victim".
I made the mistake of engaging such a woman on a BS site, because she seemed so earnest about wanting to know "why", so I told her my theory of humans not being monogamous creatures by nature, and that marriage is a social construct created when our average life span was 30-40 years, and that spending 15-20 years with one person is one thing, while 50-60 years is quite another and often leads to frustration and resentment (and cheating). I also explained to her that I really loved the MM in my scenario, and that we were on most accounts a better match than our current spouses, and she completely lost it. She hurled every insult you can imagine, dug up every hurtful thing ("you're delusional if you think that's love", "you are nothing but a whore", etc.), which made me think I'd really struck a nerve - she's hellbent on believing her own narrative, and no amount if "information" or "truth" will satisfy or help people such as that. In fact, it made me feel sorry for her that she was that unable to see her own likely role in driving her husband away from her, because I doubt that sort of controlling, possessive behavior is new to her. There's also a lot of "communication is key" type advice, assuming that it hasn't been attempted. Like, dude, when you've tried Every. Single. Way. of communicating your issues and trying to resolve them with honesty and reciprocity, and NOTHING works. Oh, now that I've been caught having my needs met elsewhere suddenly "communication" and "honesty" is important?! But it wasn't when I was faithful and trying to do all the "right" things?
I'd say, if you are intent on sacrificing your own happiness and the only life you're given to "save face" in front of friends, family, and neighbors and stay in your shitty marriage, you best continue to live a lie, through and through. Too many people prefer the comfort of the pain they know over the uncertainty of a future with a person who makes them feel alive, and a lot of this is framed as "you're just going to end up having the same problems in the next relationship again". It's like some sort of Stockholm Syndrome. I mean, I'd be a hypocrite if I said I wasn't currently in that situation myself. My excuse? "Waiting for the right moment..."
So that's the long version of "why telling the whole truth isn't always the best plan"...