I will address them in the order that you presented them:
Riven
Yasuo
Garen (you can't deny that regen)
Mundo (the new freelo, albeit not mobile)
Katarina
Tryndamere
Rek'sai (pre-nerfs)
Renekton (2 free dashes, innate sustain, while being tanky)
Riven:
- She falls off late game, when others are just becoming ridiculous. She's a lane bully and a mid game carry, after that if you can't deal with her it's not Riven being broken it's that you don't have the tactics.
Yasuo:
-Currently in a broken state, as is Tryndamere, solely on the fact of some masteries and a passive that gives him 2x Critical Chance. However once he's out of lane Yasuo severely falls off, he only dominates lanes and I expect to see nerfs in the future.
Garen:
-Zone control

Mundo:

Katarina:
Heavy CC:

Tryndamere:
- He's pretty ridiculous right now however
work pretty well
Rek'sai:
Pre-nerfs
^ This is not even remotely relevant since it's been addressed.
Renekton:
as well as armor based items
Why are the a good # of them hyper mobile with insanely low CDs and free stats/passives/sustain all through their kits?
Which of them truly PAY for being resourceless?
They are hyper-mobile and have low CD's AND huge amounts of cost for the small pools of Energy that they use.
You can build him one of two ways:
- Basic Attack Oriented
- AD Caster Oriented
If you build him #1 then all you need is to build armor and use CC. He needs to get close and to get close he needs to expend his escape or use an activated item, as well as using energy.
If you build him #2 then
can be used to mitigate most if not all of the damage output from Zed.
See the thing you're failing to realize is that most energy champions have high prices to pay that aren't on a bar or immediately obvious. Dig deeper and you'll see that Manaless champions often get the short end of the stick especially in prolonged team fights.
Before you say i'm a energy/rage/cd champion user just trying to make excuses, check my match history you'll see happy bird emperor. http://www.mediafire.com/convkey/9e73/bmjbc26mdfsgjuszg.jpg