I think they should always reward the apropiate amount of experience and even gil. This goes beyond if a new system is targeted or not to all players, it's just a basic concept for a MMORPG when you ask the player to invest time in any activity.

So while the main purpose of this feature is to replay the MSQ for the story (and that's a reward already if you really like it), the time invested while doing it should always be rewarded in a practical way, and that means experience, even if it's not the same amount as the first time you did it.

And i'm not even saying that it should become an efficient alternative to level other jobs, but it certainly should be an option to add variety to that process.