You would still deal with the deliverability challenges of getting your private email server trusted by everyone. It will work 95% but there are a bunch of weird edge cases due to old IP blacklists, bad spam rules, etc that will cause you problems and basically require a greybeard email expert to diagnose and fix. Sadly, I think it's just too hard to run your own email server these days.
They could also provide Cloudflare-like spam and DDoS protection for receiving mail