First of all, this isn't a brand new idea that I thought of myself. Basically, these pairs & teams are kinda like your encounter with special creatures in the forest, but with a higher chance of encounter. They are "events" that just pop up & force you to fight.
Watch out! You have encounter <pair/team>! [Fight]
List of pairs/teams:
Oboro and his team (Oboro Lv4, Mubi Lv4, Kagari Lv4)
Gato's Bodyguards (Waraji Lv4, Zori Lv4)
The Demon Brothers (Gouzu Lv5, Meizu Lv5)
The Sound Genins (Dosu Lv7, Zaku Lv7, Kin Lv4)
The Kamizuru Clan (Suzumebachi Lv8, Kurobachi Lv8, Jibachi Lv8)
Team 8 (Hinata Lv9, Kiba Lv9, Shino Lv9)
...Sound Five, The Shinobazu, The Snownins, Ino-Shika-Cho, Shiitenshounin, etc.
These guys have higher stat than when you encounter them seperately. They may not look like much of a threat right now, but once they have jutsu & special attacks...
For example, Kin lowers your stat with genjutsu while Dosu does his special attack & Zaku use his "jutsu". Shino drain chakra while Hinata does multiple damages & Kiba doing heavy damage.
I think this would be better than sudden death after a number of flawless fights, no?