Let's get the largest and most contentious genre out of the way, shall we? I expect a lot of different answers here, because this genre is one that has actually seen its breadth and variety go down with time, like a funnel. Meaning that there are a lot of what I would call "homeless" MMO veterans.
I don't expect my personal answer to necessarily be popular, or to even necessarily be considered a true MMO (it's more MMO-lite), but I really do think it's an unserved niche. It's where I would consider myself "homeless."
My MMO would be a fully instanced world full of tailor-made challenges. It would basically be Guild Wars 1 with specific modernizations such as map modifiers, weather effects, improved companions, and passive trees.
The purpose of instances in a MMORPG is to create specific challenges for groups of players, and the nature of these challenges simply are not possible in an open-world setting:
1) Players will need to consider their skill bar and the skills of their teammates for all challenges in an instance prior to entry. All skills will be locked down while in a mission.
2) Instances will include a variety of enemy factions that each use the same kinds of skills that are available to players. Players will need to counter these to succeed on higher difficulties.
3) Every instance in the game would offer easy, normal, and hard difficulty modes. With the exception of Patrol maps.
4) Patrol maps are instances which provide drop in a drop out MMO-lite zones with dynamic content. Like a Destiny or Marvel Heroes patrol zone. Normal skill bar restrictions would not apply and AI companions cannot be brought in.
5) Instances will have unique, rotating modifiers, such as enemy fire auras that change out daily.
6) Weather can impact specific instances on a timer. Rain, for example, could greatly ramp up water and electric damage dealt and received while weakening fire damage.
AI companions will be available as party options for all missions except Patrols. These function like Heroes in Guild Wars 1, except with personal quests, romance options, and writing akin to a classic Bioware companion.
The game would offer hundreds of skills to choose from, but limit your skill bar to 10 skills, with one elite skill, at any given time. These would fall into schools of magic (rage, fire, water, air, lightning, psychic, nature, etc.), and two different schools can be mixed in a build.
The game would not be strictly action oriented. Functions like dodging and blocking would be tied to specific skills, meaning that they are available if desired, but come with an opportunity cost. The game would never be intentionally designed to test player reaction times.
Progression would be purely horizontal. There are no player levels, and gear progression would focus on different but equivalent modifiers. For example, one sword might increase all fire damage you deal, give you bonus fire damage on basic attacks, and grant you a permanent sunfire aura. Another sword might grant you lifesteal on hit, increase healing output, and restore mana over time.
Additional horizontal progression would be available through skill hunting. Different boss mobs throughout the game would have different skills, and defeating them will acquire the skill. Unlike its inspiration in GW1, no Signet of Capture or equivalent will be necessary.
There would be an extensive passive skill tree akin to Path of Exile. This would be a vertical progression element to a point, but would eventually cap out and never be increased. This tree would be complex, but freely refundable. It would also have speciality nodes unlocked in the same fashion as skill hunting. Each school of magic has its own tree, but only your primary school will be available).