Having never played any major MMO apart from this (Ragarok Online, Runescape and Maplestory don't count, >.<) my experience with jumping around with other players in the vicinity is severely lacking. But, the ff games have had a good use of jumping and swimming in their games. Final Fantasy X comes to mind, with both swimming and jumping in the original and the sequel respectively. Final Fantasy XIII also did it pretty nicely with jumping as well.
So I kind of, for better gameplay, that jumping free-reign to not be implemented, even though I have nothing against it, but just to prevent those who dislike free-jumping. Instead, keep it to certAin areas where players are prompted to do so, such as on platforms or off a cliff or through steep terrain. Keep jumping for an ideal purpose; add it around certain land masses that would just look odd if you slid down the side of it, like some parts of Thanalan and La Noscea. That way, it won't be abused while still serving a purpose in gameplay. Those who just want eternal jumping can park their a*ses there and jump for all they want.
Alternatively, they could implement free jumping, but have it on a timer, as well as restricted in certain areas, such as cities, hamlets, camps etc. Will still have some degree of annoyance for those absolutely detest jumping, but it can be a compromise otherwise.
Another use for jumping I thought about was in combat, a manual form of dodging for certain skills that enemies use. There would probably also be a timer, to prevent abuse, but used this way it could have some pretty neat battles as well as strategies to be had. Of course, other limitations that the 'battle dodge' should have is that you are in active mode and are currently engaged with an enemy. But with some thought, it could certainly have some engaging battles.
Then we get swimming. I always thought the FFX swimming was a nice touch; it could be similarly brought here, used to trasverse unknown locations and explore the world more effectively. Limitations could include time spent under water, and taking damage after a certain exposure under water unless you come to the surface for 'air'. Other ones could be not able to change class (certainly not changing clothes underwater), type of armor you're wearing (fully plated person should NOT as fast as a person in a bikini) and your chocobo. I personally see swimming as a way for gatherers to shine a bit, harvesting fish, sea plants and oceanic minerals. There could also be underwater fights with certain monsters, which would provide a balance for those wearing full armor to those in a subligar. Certainly, underwater activities should not be a main, but it can definitely add for some engaging and fun content.
So all in all, it really depends on how it's implemented. I personally don't mind either way, but for those who are against and those who believe jumping is their true gift, its something to think about; the word compromise.