Ok so what about a 2d beat-em-up game where the power of your attacks is influenced by how cool it looks.
A game where arbitrary backflips are more than welcome in making your attacks stronger.
For example, let's say you encounter an enemy.
(Click on images for full size.)

You throw a grenade behind them,

propelling them towards you,

then punch them midair.

Now in real life you would probably just end up injuring yourself.

But physics bends to the power of cool, thus allowing you to land a massively powerful blow, as well as leaving you unscathed.

Because launching someone at you with a grenade and punching them in the face is pretty damn cool.

- The player's attacks are stronger the more stylish they are.
- The player would be able to grab and throw enemies/weapons, and do various acrobatic manouevres.
- Holding click would hold your sword out in the direction your mouse is pointing, and moving your cursor around would cause the sword to swing.
- You could use these mechanics to perhaps fire a shotgun in the air mid-flip, or hold your sword in the air for a falling enemy to impale upon.
- Your character would become stronger by spouting one liners and dressing fashionably.
Story stuff:
The game would start in a nation ruled by a terribly oppressive, yet rather cool government. The populace is forced to live like pansies in order to keep their power in check, but an uprising finds its way to your village. Chaos ensues, but soon one of the upper divisions of the ballin' corps arrives to quell the rebellion. The considerably less awesome rebels are quickly defeated. Their leader, the only one left, valiantly fends off their forces, but alas is overpowered. As he is cut down, his cool-looking knife slides across the ground to you. You take the knife, and that's where the game begins.
Throughout the game you would amass an army, with your power snowballing as you journey towards the government HQ. You essentially ride a wave of badass into the capital, destroying everything in your way, and after that who knows.