Pfft this is what I was alluding to earlier. What people say they would do in an infidelity situation - and what they actually do are often very different things. I used to think like you and was very definite about it, but each situation is different. And so much depends, post-discovery, on the actions of the person who has hurt you; how much they change as a result and how confident you are that this could never happen again.
I can tell you that hurt pride often gets in the way of a considered decision, which is why I urge people to seek information, ask questions and listen before deciding.
And that whenever infidelity happens, unless the character weaknesses of the unfaithful party are eradicated, there is always a chance that this will happen again. Having been through this once, most people can allow themselves some certainty, that they wouldn't forgive a second time - and I think that's the sanest response too, because once the unfaithful spouse has seen the hurt and destruction, to do it again smacks of sadism and an intention to hurt.
A distinction needs to be made too between the verification you are doing now with the chat logs (and I know I keep suggesting it, but phone bills too please!) - and the notion that you will be doing this forever more. If you both learn from this and heal well, you won't be forever snooping at all.
When someone has just come out of a deceitful situation, they are in the habit of lying. As you have discovered with your H, he told lies after discovery too. In this situation, it makes absolute sense to verify everything.
I scratch my head and wonder why anyone would consider making such a life-changing decision, without all the facts to hand? Even in a business decision, if a colleague or competitor had been deceiving and lying to you, you wouldn't continue to trust what they said and ignore other incontrovertible sources of information, would you? This is even more important.
Let me share a little of my experience. Despite the fact that I had a gut feeling there might be an affair, 6 weeks before discovery I did the grown-up thing and asked my H if there was anyone else. Even at the time, it seemed an utterly bizarre suggestion because I'd never had those instincts before and of course, this was met with a denial.
I didn't snoop then or before. I believed him totally. My accidental discovery was made when charging a lost phone, which my H had given to our DS weeks earlier and which I had found at the bottom of a cupboard, where it had been for 5 weeks. The shock was enormous and horrific. After that and the subsequent confrontation, having never invaded my H's privacy in what was by then 24 years of marriage, I snooped with impunity. My H knew that I was doing this and gave me complete access to everything anyway. He understood why I was doing this.
Over 2 years on, I cannot remember the last time I verified or snooped on anything. I trust him completely. My life and the people we are now, are very different. I think hell would have to freeze over before my H would do anything to hurt me like this again, but he knows if he does, there will be no second chances.
But by God if I had my time again, I would have snooped once I had some suspicions and would advise anyone in that position to do the same, before and after discovery. People's mental health is worth far more than some noble desire to respect privacy.