Isn't personal taste a funny thing? Because I thought the author handled it beautifully, especially in this case where Harry and Severus both clearly love one another, and this anonymous third person means nothing more to Severus than a habit.
But of course, it's my opinion that confessing to such a thing is generally a selfish act---the offender seeking absolution from the offended---and not something that would have been done for Harry's benefit. If Harry had known, it would be another story, a confrontation would have been inevitable.
Could Harry and Severus's relationship, the way the author has written it, survive the infidelity fall-out, if it were revealed somehow? I very much think so. But as it was handled, Severus came to his senses, realizing what he'd put in jeopardy was far more precious than the minor, habitual gratification. Whatever Severus's motive(s) for doing it (and I think it was his own insecurity, his unwillingness, or inability, maybe, to believe that someone such as Harry could actually love him so completely) ceased to be relevant. Harry hasn't lost anything at that point. In fact, he's gained something. And telling him about it now would only do damage.