Rampant generalizing. Not all TKD practitioners exclusively pick the back leg. This is like saying that Karate people only like to punch with their left hand. Ridiculous. Whether a kick is stronger thrown by the back leg or front leg is dependent upon footwork, hip torque, and individual's strength, NOT by whether you practice karate or TKD.
2. Regarding power, the Karate kick is by no means weaker than the TKD kick, In fact, in many aspects, the Karate kick is stronger. TKD uses the back leg as their principal means of defense as well as attack, while Karate uses the front. Front leg kicks are not only faster than the TKD back leg kick, but if used in a slide or pull, twice as strong.
What kicks did you "invent"? Kicking arts have been around for a while. I doubt you have discovered anything that someone has not tried before.
3. I don't know where anyone gets this impression that Karate martial artists are extremely stiff, rigid , and traditional. This is not true. Karate is an extremely flexible art that can bend to accomadate new kicks, new stances, and new blocks. I know from personal experience. I've invented several kicks myself (Not exactly practical I might add, but rather rewarding when you land :) )
No one will. See whether something is effective or better depends all on the individual and how they train it. You are obviously a beginner, but hey, better to get educated here than by some irritated TKD fighter who you would have eventually pissed off.
Now, if anyone can tell me how TKD is better than Karate, I promise I can counter every point effectively and clearly. Maybe I can earn my art the respect it deserves around here.....