To put them in other words: the 3rd role of the trinity, DPS, occupies an odd position in which it is reliant on both healer and tank while they rely on it, and yet its role is very long term. Most often the DPS role is considered the most "fun" (I know plenty of players enjoy tank/healer, but the clear abundance of DPS in LFR and Dungeons shows that it is indeed the most played). I believe that this is because DPS is perceived as the "least accountable" role because there are usually three of them (or more) and one poor DPS can be made up for by two good DPS. In a way the tank and healer are "independent" of the DPS in some ways; the tank and healer are connected, while the DPS does their job mostly ignorant of the other two. Right now DPS feels like an outlier, so my thought experiment as follows is converting the DPS to a role that more intimately acts with its companions.
Before I can do that I want to clarify what I view as each role's purpose and, well, role.
Tank - The tank absorbs damage and keeps the attention of the mobs. In my ideal world the tank is trying to weigh threat and survivability, while also positioning the mobs for his party.
Healer - The healer is keeping everyone alive but that doesn't mean they have to use direct heals (eg a Disc Priest in WoW using shields). A healer model can involve "firefighting" or a dwindling resource set.
DPS - Kills the monster by doing much more damage than the other roles.
What to do with the DPS...
Right now DPS is a very selfish sort of playstyle but I don't mean that as a judgment on DPSers, I play one myself and enjoy it. However the priority and rotation systems encourage a DPS to tunnel-vision on their target and focus entirely on getting the highest DPS number they can possibly get. This often requires they be more or less independent from the healer and tank; certainly they rely on the other two doing their jobs to succeed, but they do not really improve or impact the duties of the other roles. A high DPS will kill the boss faster, thus stressing the healer less and requiring the tank to make fewer survivability decisions, but in the short term the DPS is mostly just shaving minutes off the clock.
So in trying to make the DPS more of a cooperative activity I look back to Vanilla WoW; that brief window in time when stuns worked on bosses. What if, the third role in a party, instead of being just a buffer, was one who's purpose was to debuff the mob at the right times such as to reduce the incoming damage on the tank to a more manageable level. Say DPS came with attacks which would interrupt the "heavy" attack from the mob or reduce its damage by 75%. Of course this system is not perfect either, and would still leave 2 people in a 5-man party with no defined role. However I think its a start, getting us towards a system in which the three roles of the trinity interact on the short term. Now we might not let everyone "stun" a boss and stop a mechanic, but perhaps if done at the right time a debuff can turn an unsurvivable attack to a survivable one.
I suggest this because personally I would welcome a system in which tanks and healers both did the same damage as "DPS" and gave the DPS additional roles to fill..perhaps they CC actively and debuff, or buff your teammates. The streamlined system of "everyone fits one of these three jobs" is starting to feel...boring perhaps. I know why we have moved this way, but I think we can make it more interesting.
Alternatively, perhaps the healer would have a very small mana pool and the DPS had the ability to replenish the healers mana, thus extending their survivability.
Making DPS a group activity...
However lets say we like keeping the third role as "DPS" and having the majority of the group fall into this pool. Previously I called DPS the "Selfish" role and I stand by that because in many ways each DPS is an island. While in games like WoW each DPS might benefit from small debuffs their friends might throw on the boss but most often these are brought by many classes. So for the most part the average DPS goes in and focuses on their rotation/priority and moves when they have to, otherwise ignoring the rest of the party. They'll notice if the tank loses aggro, but for the most part a DPS can play through most fights without a second care as to what the rest of their party is doing.
So I am going to don my
When these sorts of combinations have been found in WoW (like the old Rogue Rupture enabling high damage to bleeds or a Shadow Priest's Devouring Plague being spread by a Death Knight's Pestilence) they are usually considered exploits and removed.
What a crazy rabbit hole we'd have fallen into if the Rogues would use Eviscerate which set the Warlocks up to Conflagration for increased damage and the Warriors could follow with Colossus Smash for "TONS OF DAMAGE". Obviously in the current raiding layout this would not work as well and would be chaotic, but Blizzard is a smart company, and it would go lengths towards making the "MMO" more of a multiplayer, cooperative experience.