DH and I are like you. We openly share phones, photos, text messages, emails, everything. We have each other's passwords and PINs to everything, just in case we may need them in an emergency.
If his phone is nearer to hand for some reason, we'll use his for whatever phone-thing is needed; if mine is nearer, we'll use mine. We share our phones' cameras and photo galleries nearly seamlessly. If my hands are full and I need to read/reply to a text, I'll ask DH to open the phone, read it to me, type the reply, and vice versa. If he's driving, he'll ask me to open his phone, scroll through the last bloody year of texts or emails to find one recipient, then type out the message - as if this mundane message were urgent and needs to be done right now so of course I can't ever have a moment's peace when he's driving... 
The only time either of us has ever tried to angle the screen away from the other is when we've been plotting birthday gifts with in laws or planning some other kind of surprise for the other.
BUT that said, I fully understand that we are not exactly the norm. We're strangely close (co-dependent, most likely, if I'm honest) and weirdly similar, to the point we're only half jokingly convinced that one of us is a figment of the other's imagination, we're just not sure which is which.
I have no opinion one way or the other on how other people conduct their phone business within their marriage and wouldn't ever judge anybody whose phone is private to them. Most people I know consider their phone to be private to them, and that's just not even my business. Sharing is just what works for us, and I have no right to and wouldn't dare try to impose my way upon anyone else or judge anyone else for the way they use theirs.