Guild Wars 2 claimed to have done away with the trinity system... it only sort of worked.
What you ended up with were classes that could feel watered down. Nobody was really that good at anything, everybody was just kind of mediocre at everything. IMO it made the classes feel indistinct from one another.
You don't have to abandon the trinity just to try and be innovative. Just make it so playing a tank or healer solo doesn't suck, and people will do it.
There's also Rift's approach, where they added a fourth "support" role into the mix. That could work well in a Final Fantasy setting too. Using FFXI as an example, a summoner, bard, or red mage could easily fill the support role. Kind of a nebulous role whose responsibilities change depending on what class they are and what the party needs at the time, but doesn't fall squarely into a tank, healer, dps (dd) category.
Cross-server parties are for one thing, and one thing only: to make queue times not stupid. If the group finder (or whatever it ends up being called) can put groups together without ridiculous queue times, then it doesn't need to be cross-server. If it can't, then it does, and you roll with it.