I had a bit of a chat and a bit of an essay and thought about it, and I realized something:
Nobody likes playing the support characters.
Nobody picks endurance if they have a choice. Speed, range, stealth - anything but a tank! Similarly, nobody wants to play a healer. I mean, sure, if the party needs one, you'll take it for the team's sake. But nobody goes "wooo! Stand around and get hit!"
Both tanks and healers are support roles. In oldschool games, tanks were combined with offensive capabilities that made them acceptable ("warrior"), but that's steadily been eclipsed by the concepts of strikers and glass cannons. The classic D&D "cleric" was a combination of both support roles - boring healing combined with boring damage-sponging.
If we dissect party combat roles, we can see that most party combat games have a few specific tactical concerns.
1) Dealing damage. Often, there are multiple types of damage, or damage of varying focus. So you can have a lot of different "damage-focused" classes that are all unique.
2) Tactical manipulation. The most obvious is the tank, who draws the enemy fire, since he's so much better able to survive it. However, there are plenty of others, such as the rogue that gets free movement, or the skirmisher who gets a second attack if his first kills an enemy, or even just someone who can dominate turn order.
3) Statistical manipulation. The obvious example is a healer. However, boosts and hexes of all kinds apply - berserkers, mage armor spells, leadership bonuses... these are most common in MMORPGs, but have migrated into all sorts of other games.
My hypothesis is that tanks and healers are not boring because of their role: they are boring because they are a boring version of that role.
In most games, the classes are split into a few simple categories. Tank, striker, support. A lot of effort is put into making tank and support interesting to play, but there's an easy way around that issue: don't have them. Come up with new roles. Roles that are all interesting right from the start.
So, fun challenge: can we create a tabletop RPG where the character classes don't specialize in any of those three groups? Where all the classes have all three kinds of utility? But, of course, all the classes still have to feel different and interesting and mesh well in combat.
I think one key would be in allowing the players to migrate between tactical roles on the fly. So Anna and Barry might be dealing damage, while Jacob and Kelvin are doing tactical manipulation. Of course, these aren't the same at all: Anna is burning stats to deal out massive damage to one target, while Barry is providing baseline disruptive damage against the mooks. Jacob is drawing enemy fire while Kelvin is popping the initiative stack so that the enemies can't get their team attacks working.
And they all have the same base amount of HP and armor.