It’s as private as your email...which probably means not private.
Like most people, I depend on an advertising company to host my emails. But I wouldn’t share my private diary with them.
I'm assuming you're speaking to higher-level issues, such as privacy or security?
A good email client can also learn to automatically encrypt when you send to a specific email, so you can send to a specific alias (with a plus or subdomain aliasing scheme).
(Also, calling PGP "the best encryption there is" might be a bit of hyperbole.)
And the company's business model is absolutely irrelevant actually. You still need end to end encryption.
> "But then will your diary service work right with it?"
Yes, it's called an email archive. It's searchable too. All you need is an email client that supports PGP. I personally use Mailmate.
And I've got email going back to 2004, while I no longer use any apps or online services from 2004 (most died).