I'll cite one aspect of its design and implementation as a problem – it doesn't support standard protocols like IMAP unless you choose a paid plan. Even then, you have to use a "bridge application". On mobile, only the official app can access the mailbox. To sum it up, if you're on a free plan on ProtonMail, you cannot export your mails out (unless you do it by "printing" mails one by one). To contrast this, even "free" platforms like Gmail and Yahoo provide IMAP access to all accounts.
But that's the point of ProtonMail. All your data is invisible to them. If you could use IMAP without a bridge app, which encrypts and decrypts all your mail data locally, guys at Proton could read your mails. Not necessarily because they would want to. That's just how email works.
I would wager any email provider would suffice for a simply diary, if thats how you want to keep it.
I'm assuming you're speaking to higher-level issues, such as privacy or security?