This is an oldie for sure, but in Anarchy Online I played a hybrid tank. It was an Atrox Keeper, who was basically a meatshield DPS Knight with heavy armor and a 2 handed sword. He didn't have any inherent threat-generating abilities (aside from a few items I'd acquired), but rather could hold aggro from a "midboss" mob while the main tank/rest of team focused on the main boss/smaller enemies.
For a practical example, suppose the Enforcer was tanking Hecklers, and a Horror jumped into the fight. I would basically solo that Horror to keep pressure off the main tank. I did so much damage that I was able to hold aggro, and was survivable enough that periodic offheals were enough to keep me going until the Hecklers were dealt with. If the Horror had attacked the Enforcer, he probably wouldn't have survived the combined incoming damage. Two full tanks would not have been as efficient damage output for our team, and be redundant.
Essentially, my hybrid tank was interchangable with a mezz/stun/calm/CC type of caster, except that a dedicated CC was more effective vs large groups of adds, whereas hybrid tank could salvage a situation if the main tank happened to go down. Stealing agg from the main tank in raids was also hella fun. 50+ people ragetyping in caps at me that I'm gonna get us all killed, and then we win. But it is a balancing act for sure, and it will take some time to explore what DAI classes can do before determining if it would be useful or effective in DAI. With 4 person teams, hybrids could certainly have their uses.
For more recent citations, Ice Crown Citadel in WotLK had fights that required an offtank, Karagga's Palace in SWtoR was full of offtank/tank swap fights. Eternity Vault had a few also.
In PvP, hybrids have always been the ones to get the most whining/nerfing, if that goes to show how good they can be. Anarchy Online Adventurers, WoW Shamans and Shockadins (Holy Shock Paladins), SWToR Operatives (and a handful of good Juggernauts) come to mind.