If you think flappy paddles make you faster on the street, you're insane or silly (or both). If you think they makes you faster on the track, you must have godlike driving skills already. If you don't already have godlike driving skills, then you are better off working on your braking zones and driving lines first.
If you think flappy paddles make you feel like you're in a race car, then why aren't you commuting in a caged, stripped out miata, in a helmet and full nomex suit? I mean, that's what you want, right? Why not go all the way? Oh, you think fast shifts sound cool.
If you think manuals are antiquated technology, why are you still driving in a metal cage propelled by small explosions, suspended by coiled up metal and oil filled tubes?
And if you buy flappy paddles because no one else can drive manuals, why not teach them? It's your bloody car, after all. Are they pitching in to buy the thing?
So why should you be driving a car with a three pedal manual gearbox?
Your foot is directly connected to the engine output. Your engine's mechanical well being is your responsibility.
You have direct control over the transmission's smoothness by modulating engagement and disengagement of the clutch. Smooth automatic-like shifts or head jerking bang-it-in shifts...up to you.
You will become more aware of your engine speed, the speed of the engine relative to your road speed, and your engine's power curve.
You will become more aware of what's ahead of you on the road. You have to think about what's coming up, and quickly diagnose what your road speed will be (and thus, what gear to use).
You will learn the joy of the sequence of braking, executing a perfect heel-toe revmatch on the downshift, and turning into the apex.
You will be less distracted (if not completely undistracted) by your Starbucks frappucino, your McDonald's Egg McMuffin, your makeup, Facebook and Twitter on your iPhone, and the morning paper.
You will have more fun.
In summary, three pedals will make you a better, safer, more passionate driver.
If you cannot drive three pedals due to injury, then I understand. Maybe flappy paddle gearboxes should have handicapped placards as a prerequisite.