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!