Actually, it is very much a game breaker. The inability to jump was annoying as hell in FFXI, too. The FF games have needed the ability to jump ever since the series went truly 3D with FFX. They were able to get away without a jump button in the PS1 games because those were more psudo-3D as opposed to the actual 3D that we didn't see until the PS2 games. A game that has 3D graphics and 3D environments should not have 2D character movement!
And yes, you can jump in some of the offline FF games. FFX-2 has a context-sensitive jump/climb button, FFXIII has auto-jumping all over the place, and then Dirge of Cerberus and FFXIII-2 both have a specifically designated jump button. So for you to go around claiming that you can't jump in any FF game just makes you look ignorant, because you can.
But regardless, complaining that you don't want jump is pretty dumb when it's already been confirmed that SE is indeed going to add it to the game eventually. Maybe it won't come until Version 2.0, which is fine by me, but it's still coming regardless. Might as well get used to the idea and stop bitching.
Don't be dumb. Jumping doesn't ruin anyone's immersion. And if it does, then that person needs to grow the hell up. If someone gets annoyed at something as simple as jumping, that's a problem with the person, not a problem with the game.
Personally, I don't get annoyed at all when I see people jumping in other MMOs. What annoys me is the people who complain about the jumpers. It's like they're just looking for something inane to whine about.
You mean they'd have to make walls that are actually of a size significant enough to make them believable barriers? Oh no! How horrible would it be to have believable barriers in the world instead of stupid ledges that don't feel believable as barriers at all! What ever would we do!?
</sarcasm>
Your argument about appealing to aesthetics is bullshit, by the way. There is nothing inherently more aesthetic about a short ledge as opposed to a high wall. Neither one is any more visually pleasing than the other as far as aesthetics are concerned.