The “secret sauce” for deliverability is _volume_. If you don’t send enough emails from your servers to each major email provider (at least 100 emails per day to each of these) you do not even show up in their reputation scoring systems which means whatever you do, you do not accumulate positive reputation score for your actions. Not an issue to get to that volume if you’re even a small ISP but quite complicated for these guys who manage only their own email.
That's not my experience; my self-hosted setup rarely sent more than 10 messages per day, but I could deliver to gmail, hotmail, yahoo. No problem, at least not since about 2009. Before that I did have a fair bit of mail dropped on the floor by the big providers. I spent quite a bit of time stressing about it. I don't think it's anything that I did that fixed it; it just seemed to fix itself.
