I do think the Jump Potion is kind of a necessary evil... but could also be a WHOLE lot better.

Take Shadowbringers; those early dungeons were freaking RUTHLESS, and that's from a long-time player. Like, if you didn't already know mechanics were coming, they were eating groups alive. I can't imagine that being your first experience as a new player.

Another downside of the Jump Potion is that I do think the game's story could stand to be streamlined even more. Hell, I just did the Ivalice storyline, and one of the quests has you getting an Anniversary gift for one of the ACTORS aboard the airship?! The HELL does that have to do with anything?

In all honesty, I would consider having them offer a new "Starting Experience" entirely. Have the player start in Mor Dhona (maybe an instanced version, before it's all fixed up, with lower level enemies), have ALL of the class trainers present, and have a more expedited story. The story doesn't even really start to "get really good" until around the time you're going to confront Ifrit, anyways.

(Also; if I'm being honest, considering most New Jobs are still balanced to be scaled-down to low levels ANYWAYS, I might even let players unlock them sooner, as I imagine new jobs are a huge draw for new players)

Finally, I would incorporate the "link-pearl" to greater effect, so that turning-in quests could be minimized. Instead of CONSTANTLY going back to the Waking Sands and then right back out again, just have it send you on more of a constant circuit.

Just my take.