I think one thing is that different people have different levels of personal stuff in their email. For some people, email is all logistical stuff and links to family photos, for others its where the most personal things are. Obviously those people are going to have different views about whether it matters to see each others’ email.
And when I say “most personal thing”, I mean, even if you’re NOT going to bitch behind someone’s back, I think it’s legitimate to randomly feel insecure about something and want to talk it over with your best friend and decide it’s not a big deal before blurting out “WE HAVE A PROBLEM AND MUST FIX IT RIGHT NOW” over breakfast. Some people would do that in the pub. Some people over email.
For the record, I don’t really need to keep personal/financial stuff secret – my SO may not know all of it immediately, but I wouldn’t mind if she happened to see.
But what is secret would be conversations with friends about THEIR venting and THEIR life. If my best friend is sharing emotional stuff with me for support in confidence (or even something more long term like an engagement or a divorce or a good or bad diagnosis), I don’t think that should automatically go to my SO, else it’ll end up going to my SO’s best friend, and my SO’s best friend’s SO, etc, etc.
Also, work stuff. I don’t have anything very confidential at the moment, but many people will deal with stuff for work that’s confidential to a greater or lesser extent, and it’d be a breach of ethics for their SO to see their work email. In fact, if you work for the department of defence or something, you can probably be arrested for treason if you let someone read your email at the wrong time 
That said, I don’t know if I’m surprised or not. I think reading someone’s email is (commonly, not always) a big invasion of privacy. But so is following them, or checking up on them at work, and even if it’s wrong we know people do those things when they’re worried about their spouse. It’s very weird to me to think of a situation where I wouldn’t be able to ask my SO what’s wrong and get an honest if unpalatable answer, but if I were in a different situation where I couldn’t, I don’t know how I’d feel.
ETA: That said, regardless of the literal answer, I think answering “no, not under any circumstances” is probably a high predictor for being someone I would be compatible with 