I don't mean more fun as in more fun at a given time, but more fun on average. One more group slot would mean one more space for a DPS. That would help with the tank/healer shortage not by adding tanks and healers, but by reducing the needed ratio. For DPS this would mean more time in groups rather than soloing with ever-increasing despair as LFG fills up with "lf2m tank and healer." For tanks and healers it would mean one more tell and invite to send out.
Loot tables would need to be adjusted slightly to accommodate the greater proportion of DPS. It would be worth it though. Not the loot table changes, but the increased DPS presence. When a tank can get a run any time and a DPS cannot, who gears up faster?
For all we say of how a geared tank makes more of a difference than a geared DPS, how much of that is adaptation, that we're used to overgeared tanks and undergeared DPS? If DPS were on par with tanks, we might start seeing how the group overall matters more. Currently we don't see this because by the time the DPS are geared up, the tanks are so overgeared that you might not even need a healer (maybe the elemental shaman tosses a couple on bosses).
With DPS gaining a larger share of loot and being better geared overall and tanks in worse gear overall, we would see a smaller gap between new and old tanks and could potentially reduce the problem of people expecting tanks to carry them. Move even gear distribution would mean that the tanks couldn't carry them, or at least not as much as they do now. This would mean new tanks would have a better chance of getting into groups and get gear; resulting in not just fewer very overgeared tanks but also many more reasonably geared tanks.
From this we'd find something really great: challenges as instances are no longer trivialized on a wide scale.