You could do this on Twitter if you stay within the character limit but for material in the link, that requires 5+ tweets to cover completely, it simply seems that the amount of scrolling and clicking is a waste. This sort of stuff is not always so neatly presented as it is on this particular link within Twitter. On your timeline, you might notice the "part 3" tweet first. Then you gotta click it to try to gain a larger context to see if its actually interesting. Then, if it is, you have to click to find the "part 1" tweet. Sometimes this will be simple because you can show the entire thread. Other times it seems like you cant. It is a lot of manual overhead to consume two paragraphs or so plus a link to the actual podcast that the paragraphs are describing.
Twitter is obviously a broken system for trying to share interesting links then. I don't see why we should ruin publishing for everyone else because twitter doesn't allow sharing text properly.