That being said, I mostly receive email, and the privacy benefits of running my own server would still be significant even without the ability to send email at all.
Re: the privacy benefits, is it just that Google (or whoever) has no access to your mail, or is there another benefit? I'm not doubting, just trying to understand specifically what you protect against? And how much is the benefit diminished, if at all, if most of your correspondents are on a BigMailServer?
Besides privacy, running your own server means you can create as many mailboxes/aliases as you like. I give each website/company a distinct alias; this allows me to revoke an alias that becomes problematic, e.g. due to spam. There are no storage limits other than those dictated by your hardware, no maximum attachment size, etc. I am immune to "terms and conditions" changing overnight that suddenly shrink my storage or put features such as IMAP access behind a paywall.