I legitimately want to know what a manaless champion, such as Riven, has as a tradeoff for being manaless, compared to mana (or energy/health) based champions that fill the same role, or with a similar purpose.
Auto-attacks are manaless.
Most basic trade-off for manaless champions is having a combo/damage pattern that's very similar to auto-attacking.
Mana is used more as an ammo system for something akin to a rocket-launcher. Tons of power right away, limited ammo so you don't just fire rockets non-stop at everything.
Manaless is more akin to a machine gun: still respectable kill potential, not nearly the same level of widespread devistation.
You can often see this in play when looking at a lot of manaless skills.
A wide range of AA modifyers are manaless passives across a very large number of champions that actually do have a mana bar. When looking at manaless champions: several also have core abilities that are, for most intents and purposes, fancy auto-attack steroids. Riven's Broken Wings, Garen's Judgement, Rumble's Flame Spitter, Yasou's Steel Tempest, Vladimir's Tides of Blood, etc.
Granted - there are a few exceptions, but that's generally the case. And it's certainly the case with Riven. Riven's auto-attacks actually do more damage per-hit than each hit of Broken Wings for the majority of a game. Riven's HP shield also does peanuts compared to the defensive mechanics available to most light fighters (where you can find 100% dodge chance, invulnerability, untargetability, projectile-blocking shields, stealth, and other means to completely ignore damage rather than mitigate it by a bit).