Having read the majority of this thread, and having skimmed the remainder, I feel compelled to throw in my two cents:
A very quick personal player history: I'm a long-time fan of the Final Fantasy series, who began playing with the first NA 8-bit release. I have played every game in the "main" FF series and have completed the majority of them. I've played many of the spinoffs, from Mystic Quest to Crystal Chronicles (haven't gotten around to Dirge of Cerberus, the Chocobo Dungeon/Racing series, or the FFXII DS spinoff yet...)
I started playing FFXI in earnest about seven months after NA release and I still play it a lot to this day. I too bought a nice, brand new computer to play FFXIV and preordered the CE with rush shipping.
I can count on one hand the number of times I've logged into FFXIV since the New Year. My nice new computer is primarily used for internet radio and for looking things up on the wiki while I'm playing XI.
That said, I'm excited about the potential for XIV and while I don't play it much now, I'm very much looking forward to the version updates and I'm not planning on cancelling my XIV account any time soon.
Here's what I would like to see in a new MMO:
I would like to see an MMO that fills a niche FFXI and XIV do not. Ideally, I would like to see harmony between the three games. Obviously, it's in SE's best interest to make three MMOs that are different enough the player base will want to pay to play all three. A lofty ambition, to be sure, but I don't think it's entirely impossible.
I personally feel that SE should consider a new MMO for the mobile platform: tablets & smartphones. ****, they could probably work out a deal with Sony so that the new PSP-phones could come prepackaged with the game.
Because I'm at work and don't have the time to develop a brand new intellectual property for SE, I'm going to take the easy route and use a retooled Tetra Master as an example of how this could be achieved.
A "new" Tetra Master could be ideal for the mobile platform. The matches do not take too long to play, the card-collecting aspect of the game is a proven sell, and it's the Final Fantasy franchise. This is a recipe for a good start.
Thousands of cards could be developed. I'm thinking possibly even a card for each "version" of cactaur, chocobo, malboro, (insert recurring but different creature here), etc. The most highly sought-after cards (I'm thinking character cards like Cloud and Sephiroth, for example) could be very rare.
I'm seeing something like this that has an affordable buy-in and is free to play, pay to enjoy. I imagine you would get a randomized set of "tier-I" starter cards, with others made available from "Trainer" NPCs. Better, "tier-II" cards could be paid DLC, but should be nothing too unbalanced nor too expensive (presuming a card could be claimed by your opponent should you lose a match).
Pie-in-the-sky, this game would have a nice, simple, user-friendly UI and friend's list. A functional auto-translator, and maybe a way to propose scheduled matches to people on your friends list would be nice.
Last, throw in some perks for XI and/or XIV players -- nothing game-breaking or foot-stompingly unfair, of course. For example, the winner of a Tetra Master match is also granted the ability to process one Auction House (XI) or Bazaar (XIV) transaction remotely from their mobile device.
Say I'm bored on my lunch break. I whip out my phone, see my friends list has some activity, and invite Player X to a match. I win, and afterward I'm afforded the luxury of buying or selling an item on the AH from the comfort of my own cubicle. This not only encourages people to play the new game at times when they can't or wouldn't be playing XI or XIV, it also encourages them to continue playing XI and XIV.
Achieving something like this would no doubt be a logistical nightmare vis-a-vis server coordination and crossover, and that's not my area of expertise in any way shape or form. Maybe the Tetra Master idea I propose above is technically impossible, but that doesn't mean SE couldn't achieve something similar.
FFXI Character: Strummer; Server: Odin; 99DNC, 99PUP, 99BRD; LS: Goonies
FFXIV Character: Strummer Sleipnir; Server: Malboro; Archer 24, Goldsmithing 20; FC: Goonies