I wouldn't really recommend a story skip unless you REALLY don't like main scenario stuff or single-player games. Heavensward was a really great expansion. Stormblood is forgettable. But skipping both to get to Shadowbringers will leave you not getting the full picture of what's going on and it's not the same if you just watch a video to catch up. It's like skipping most of a book just to get to the climax and not really knowing who the characters are or why they're doing things. The rest of ARR is a bit of a slog, but as soon as you get to the final (like 45 minute long cutscene) and then start Heavensward, the game picks up more and you can tell that they learned how to pace better.

But I don't personally believe the end game in FFXIV is good enough to justify skipping the rest of the content. I look at FFXIV as a longer FF game that has multiplayer elements and weekly tasks for in-game currency.