How can I feel reassured to trust him once more
You probably won't. Not if you've got your head screwed on - why would you? You now know he would cheat on you. And not because he was desperately unhappy, or because you never had sex and were at each others' throats, or that he thought you didn't care anyway... no real reason except he could and he didn't love or respect you enough to say - no thanks, I'm married and loyal. He's not loyal. The only way you can tell yourself you can trust him now is to basically gaslight yourself.
What I keep grappling with is that many marriages do continue. I can't see how they can ever be the same.
No. They aren't. For reasons above. The people who stay are choosing to stay with someone they no longer trust. All sorts of reasons: fear, finances, convenience. But - not love, really. And certainly not because, ever, trust. There is no real trust. What there is, of course, is fury and hatred - lots of that. So you have to make a positive choice that fury, hatred, miserable times and distrust are preferable to the huge upheaval of divorce.
He would still be at it if he had been more careful, then?
Stop blaming her, by the way. It won't help.