We definitely understand that having this type of feature would make it more convenient when leveling up a secondary character and such; however, the cutscenes within FFXI were not originally programmed to include a feature to skip them and there is a high risk that new bugs may arise when attempting to add this.
For example, there are cutscenes in which certain flags are turned on while you are viewing the cutscene, but by skipping it there could be a glitch with the flag itself that prevents players from obtaining rewards even if they have completed the quest.
Since there are enormous amount of cutscenes and quests in the game, this is a feature that we unfortunately cannot address.