I think your main mistake is this:

Deterministic system - Wikipedia, the free encyclopedia

It is a very common mistake of human cognition. You will see it repeated again and again if you read this forum and the forum on Relationships and Communications.

By making this common yet huge mistake in your way of thinking, you disallow the possibility of chance.

Think of the success of Starbucks: did it happen because they took all the correct steps in all the right order, and only that? Or, did they get a helping hand from what is called "luck"?

...

Your title asks for answers. That might mean two things: 1) you want to answer the query about why your wife is no longer sexually attached to you, 2) you want to answer the question on what your next steps should be.

So, to (1) - very likely it is due to randomness, a.k.a. chance. You should stop trying to connect your behavior in the past with your wife's current state of mind. She might have grown to treat you the way people treat brothers in a nice way, and the way people cherish and value the parents of their children for their being good parents of their children, without sexual attraction, all on her own, without any assistance on your part. The fallacy of believing in the deterministic model makes you discount the possibility of chance, even though, when you check traffic on highways and learn of accidents, you probably realize that traffic accidents happen due to a wide variety of causes but also due to chance (lack of luck).

You should also see that your wife's reaction is in no way symmetrical to your past behavior. You engaged in deceit while she openly acknowledges her desire to either separate or have an open relationship. She has not engaged in deceit, so it is not the case of her reflecting your past behavior back to you. So you should stop the line of thinking about your deserving or not deserving it altogether. Plus, she is not doing anything bad for you to use the language of "deserving" - she is not being deceitful, she just wants to change the situation for the better.

You should probably try an open relationship over a trial separation because you both enjoy each other's company a lot (she, in non-sexual ways, but still), and, it would be easier to parent your small children while living in the same household. perhaps an open relationship will lead her to becoming more sexual with you, because opening the relationship will put a stop to her current agony in which she feels bound to you against her will, and people in general do not like lack of free will (in general, not always).

You said that you are a perfect husband and that you finally start reading books after a 20 year hiatus. If that is the case, I suggest you read or re-read one of the comedic masterpieces of the 19th century, by Oscar Wilde:

An Ideal Husband - Wikipedia, the free encyclopedia

After that book, read some more good fiction - do not limit yourself to reading books that, you believe, somehow help find the answers for the current situation, because it seems that the books you have chosen to read are of self-help "genre" - right?

You should also make sure the T is good, because the original T, in "immediately knowing" that you had "sexual addition", right off the bat, was unprofessional. The current T who suggests that you just have sex whereas your W does not have any desire seems unprofessional as well (or, out of touch with reality).

Finally, yes, you should stop fighting for the wife you love so much in that you would be fighting a losing battle. Instead, embrace the idea that you can continue to love her, on some level, even if she does not do what you want her to do - in reality, what you want her to do is appreciate your efforts at staying faithful and return the favor by being sexual to you. This is very much like "conditional love" - you do X and expect a prize for your doing X, especially if doing X is difficult for you. It is possible that what she wants from you is unconditional love - meaning, that you would be happy with the fact that your wife exists, regardless of sexual favors or statements confirming that she is in love with you.

To sum up, the situation does not seem to be catastrophic - there is no crisis, no abuse, the children are happy, there is enough money in the household for expenses that go above and beyond the basic food staples (counseling), and you are just going through the process of re-defining the status and dynamics of your marriage in a way that seems cooperative, overall. So nothing horrible is going on, at present.