My spouse and I have a very loving and trusting realtionship. We don't lock our phones. We don't have passwords on laptops. We don't have seperate accounts. We are able to trust each other because neither of us need privacy because we aren't fucking around.
The issue I have with letting my partner read my email or texts is mostly context. A conversation moved from in-person to text for example would be incomplete so could be misconstrued and then you're forced on the defensive for no reason. To give an extreme example...
Extreme example: Lets say you and a BFF watch some show and a main character yells "BEST COCK EVER!" for some reason... You and your friend start imitating it for laughs... Friend texts you the next day out of nowhere "BEST COCK EVER!" and you text back "BEST COCK EVER!" Without context how would your SO take those messages? Sure, you have a perfectly reasonable explanation but it shouldn't need to be explained, and initial judgement could still leave lingering "I wonder if the explanation is true..." feelings.
Friends also tell each other things in confidence and just because someone is in a relationship shouldn't mean telling them something automatically means their SO knows as well. If my best friend tells me about some relationship issue it is none of my boyfriend's business because it was told to me alone. Allowing an SO to read all of your communication is breaking trust with your friends who would have CC'd your SO if they wanted your SO to be part of the conversation.
Finally, being in a relationship doesn't mean you all of a sudden stop being your own individual person... and there are some things you just don't want to share with an SO for whatever reason that have no baring on the relationship. The reason isn't important, if you don't want to share something that's your prerogative as long as it doesn't affect the other person in any way.
I've been with my S/O for almost 8 years and we're perfectly happy, haven't had a real fight in years, and trust each other completely... Still have passwords on everything.