Now that you mention it, Shadowkey was the first game to feature the Falmer, or at least an interpretation of the Falmer in the form of the http://www.uesp.net/wiki/Lore:Ice_Tribes. These are without a doubt an interpretation on the Betrayed Falmer, though, seemingly somewhat more advanced, perhaps a sect that has risen in intelligence as suggested by Gelebor? In any case, I think the Betrayed Falmer could certainly factor into a Hammerfell game. Perhaps the recent Falmer raids on surface settlements, in addition to the devastating civil war is why the Nords could be flocking to places like Jehanna and Dragonstar, trying to make a better life for themselves outside of Skyrim? This would in turn heighten tensions between the Nordic and Crown clans in northern Hammerfell, perhaps made worse by militant Nordic reavers that intend on driving the Redguards from what they claim to be their ancestral holdings. The two sides would eventually be forced to work together when the Falmer endanger Dragonstar, potentially even besieging the city. TES VI could try and tie up some loose ends left over from Skyrim, the civil war for example devolving into a quagmire of madness and bloodshed, the fragmented Stormcloaks fighting entrenched Legionnaires, while both sides are tormented by Falmer and Forsworn. A war such as the Rebellion would certainly produce more Ulfric-wannabes.
Honestly, I've been recently looking into the plausibility of Black Marsh as a setting for TES VI, or any future game within the current story arc. Black Marsh would by far be one of the most difficult, and without a doubt the most strange province to tackle, just because how alien it is. Black Marsh's many deadly diseases and poisonous gases would be countered by the player character ingesting Hist Sap early on in the game, becoming sort of an agent of the Hist hivemind, an outsider, or, if an Argonian, a Lukiul, untainted by the corruption that has taken hold of Black Marsh. This chosen hero would then do the Hist's will, gifted not just with the ability to fight off the Hist's defense mechanisms, but also to understand Jel to a degree. Essentially, only an Argonian, one with a connection to the Hist, can survive Black Marsh, and Argonians aren't just hatched. They are made through ingestion of Hist Sap. Along with this, the player character would rely on their connection with the Hist to fight off the various threats they might face, slowly mastering shamanic powers, using their connection to the Hist to influence other things with a similar connection. Be it flora or fauna. Perhaps a trailer shot of a battle, where the hero is bested by an Argonian abomination, only to enter into a trance, ripping the monster apart with roots and vines, offscreen of course.
Another thing I think they could do to make Black Marsh more appealing as a setting is bring in some as of yet unfeatured Great House players. The southernmost regions of Morrowind, such Arnesia and Deshaan, were hit the hardest during the Accession War, and it is likely that they were lost to the Argonians, the disputed regions becoming a vast no man's land between Morrowind and Black Marsh. These regions would incompass the Dres District and the southern Hlaalu District. http://i.imgur.com/x5gs5fY.png, still being on the Grand Council, would probably have some kind of presence in the region, perhaps scattered into various tribes, engaging in guerilla warfare against Argonian settlers. On the other hand, there is http://i.imgur.com/3RRvEJk.png, the upstart that took Hlaalu's seat on the Grand Council. It wouldn't be much of stretch if they gained some of Hlaalu's former holdings as well, and Narsis, their ancestral seat of power, would certainly be desirable. Tear and potentially Narsis could be featured in a Black Marsh game, bringing some Great House politics into the mix and potentially revisiting one of the more interesting and eye catching elements of Argonian culture: the slave trade. Only, instead of the abolition of slavery, it would be the threat of the return of slavery. A conflict between Dres and Sadras could arise, Dres endangering Sadras' monopoly and vital trade routes.