Subject hits close to home.
About 6 years ago during my first really serious relationship, I checked my SO's phone after it beeped when she was in the shower. Didn't like what I saw (dirty, inappropriate texts from a supposed client). I didn't see any responses from her.
That led to a shit storm of allegations. She claimed that she was being sexually harassed, etc. and I didn't really buy it. The end result was the destruction of the relationship because I never really trusted her after that.
Fast forward to modern day, I'm happily married and my wife and I don't check each others phones (nor really feel a need to). I think we peeked a bit early on in the relationship but not recently.
When a SO is up to no good and you are checking their phone, usually there is something else or other suspicious behavior going on (where there is smoke there is often fire). So in those cases, I suppose that there is nothing wrong with checking but you really should expect the worst and be careful what you wish for because you'll prob find something that will blow the relationship up. In that case though, I think its for the best obviously for the person doing the checking.
From a personal standpoint, I'm sure glad that I checked because it was something that had been bugging me big time. At the time, I just had a nagging suspicion that something weird was going on - like at night sometimes I wouldn't be able to reach her at all even though she was supposedly "working" at like 9 PM at night, etc...
Even though there was no concrete evidence of her cheating, I confirmed to myself that she was putting herself in these situations with all sorts of men because of her role in sales for a company and I just didn't like it at all. I made the decision then and there that it wasn't something I wanted to stress about for the rest of my life (e.g., wondering what she was up to at night on sales calls, social events, meetings etc.). There was enough grey area there for my mind to run wild and conclude that the relationship was heading in a toxic direction. I don't regret the decision at all.
When you find the right person though, it seems like you just know or have the trust in someone that they aren't up to things like that. Usually this comes with time and age. As you get older, you associate with less people of the opposite sex in social situations so the opportunity isn't really there.