It was called RSS, and there were plenty of free and paid providers who would host your feeds and even feed content (like podcast audio) for you. The most popular was called FeedBurner, and you can imagine what became of it:
You are comparing this frozen-in-time 2007 (pre-iPhone!) UX to your modern ideas of publishing workflows. The RSS ship has sailed, and that’s why I am explicitly talking about it in the past-tense here. It’s important to not forget the things that came and went, lest we convince ourselves that that’s how the world has always been and start mistakenly speculating about why a particular category of thing has “never existed”.
https://en.wikipedia.org/wiki/FeedBurner
https://support.google.com/feedburner/answer/79408?hl=en