> It's possible but quite hard to run your own e-mail server; if you're not on a major provider, the possibility is high that a major provider will at some point have deliverability issues to or from you due to automated anti-SPAM measures.
In the roughly 25 years that I've used shared webhosting to have my own domainname and mailboxes, deliverability was never an issue. Never tried to send thousands of mails though, so...
I have been running web services for around 22 years I believe. At the very beginning, I had zero problems with deliverability to most addresses. However, even early on, I do remember plenty of forums that mentioned that Yahoo! or Hotmail tended to drop their confirmation e-mails into SPAM. Smaller operators had an advantage in being lower volume; I think that gives you a higher likelihood of delivery. That said, their emails are also more likely to get caught up in SPAM filters without remediation.
Something has changed recently, though. I have found it increasingly hard to even get an IP that is not blocked anymore. I recently migrated a VPS that was almost 10 years old that was running its own e-mail services, and after a lot of struggling... I gave up. It now has to go through an SMTP proxy to send e-mail. This bums me out, but after multiple attempts to get an IP that worked, I gave up. The provider did tell me that I was grandfathered in to have outgoing SMTP enabled on my servers (something that new users do not have by default, by the way) but recommended I stop using it.
Is the network open? Yes. Does everyone have deliverability problems? Probably not. But maybe another question: If you did have deliverability problems to some major provider, would you even know about it? If you're not very high volume, maybe not!
In the roughly 25 years that I've used shared webhosting to have my own domainname and mailboxes, deliverability was never an issue. Never tried to send thousands of mails though, so...