This game really lacks actual solo content. Most is either doable easier with a group (Palace of the Dead, FATE's etc.) or outright group-only (dungeons, if you want experience). There was added the squadron content now, but that is not only very early phase (the squadron cannot even properly, as in, fundamentally, do their job on the lvl50 dungeon), but it also demands other skills than individual progress.
The lack of solo content is part of the problem as to why the players skill level on average is so low. Without anything to challenge, make a player learn their class properly, they are not very likely to learn. Throwing easy content at them will just make them think they are "good". Throwing group content will pair them with good players (making the run smooth and them think it was thanks to them too) or with bad (making the run a tragedy, making them think that the others couldn't keep up).
Hence, why I'd like to see more solo content that would not be made vastly easier with a group, that would put to the test the players individual, actual skills.
The game have some interesting instances. Plenty of duels that require some individual proficiency. Then there is the mock-up battle between Ishgard and the three Grand Companies that was a wonderful mini-game (alas, a joke as a healer). Then there is another "group battle" with that war over the steppes in Stormblood. The latter two would be great content to add (solo with NPC's, as it would take ages to make sure that one could actually complete the bonding in the steppe war, at least).
The former brings to mind...a coliseum. There is already one, in Ul-Dah. But players cannot participate in it (except as part of Paladins job quests). I think it would be a great content to add however. How would I want it to work?
Battles:
Duels: Player would fight against an enemy one on one. The enemy could be selected from a list (with varying classes, difficulties etc.) and depending on the selection, the rewards would differ. Make some really challenging foes that give good rewards (experience, really), and players will really want to get better at their class. However, please...Don't think that "Bigger HP = Bigger challenge". Use mechanics for controlling the difficulty, not the enemies health pool.
A random mode where the duel takes place against a random foe would be nice bonus.
Team Battles: Since there is this coliseum, why not? The more players there are, the more NPC's they fight against, making for the content properly scaling in difficulty with party. If the gladiators will actually focus on one target instead of going through enmity list as normal, that is. Meaning, people will probably die, but their goal is to kill all the opponents before they all get downed first. It's a fair game for either side. Again, opponent selection or random.
Tournament: Well, self-explanatory. Could have either or both of two ways it's calculated. Elimination, where you lose, you're out, or point-based, where you gain point for draw, two for win and naught for loss, and you'd have to fight against every opponent once (so seven/fifteen duels). The further the player goes/the higher position they end up as the higher the reward.
Adding extra player teams could be available, with the teams being as far apart as possible with the amount of people (if in elimination tournament), so that if there are two teams, they can only meet in the finals.
This could also include a way for players to organize tournaments, putting an item as reward and inviting others to participate or making it open for anyone, though NPC's would still fill-in the blanks. What happens with the reward if NPC's win? Well, details...
And yes, duels or team battles are fair game.
The important part is making these duels a challenge. Not a roflstomp that the bottom-skill players can defeat, but something one needs to be at least decent for the weakest NPC, or a "real pro" for the highest-difficulty match-up of highest difficulty NPC. If they are not a challenge, there would be no improvement in individual player skills, and it's just become another good or bad but way to get experience.