With the simplest tools, the most amazing things can be done. An artist can have access to the most powerful imaging technologies, but truth can still be shown with a simple brush and paint. The trappings can often get in the way. Martial arts is no exception.
What draws many people to martial arts is the style and flash. Spinning backfists and sacrifice throws. Of course they have their place, but perfection, to me, is rooted in simplicity.
The more advanced students at my jujitsu academy seem to have a few techniques that they work on religiously. I personally only use four or five submissions and 90% of my taps are from one of those submissions. Wrestling is much the same. I have a few takedowns. They are mine and I can transition between them seamlessly. They are simple and everyone knows how to defend them, but I drill them. I tweak them and make small adjustments until my execution is just a little bit sharper than my opponent's defense. And that is where I win.
I am relatively new to striking, but I apply the same principles. I sit in front of a bag and throw jabs. Throw it out, leave the arm loose, tighten the fist, shoulder impacts the jaw, hit with the right part of the fist, bring it back straight into my guard. The first punch most people learn is deceptively complex. I pawed at the air, or the bag, for six months before I threw my first decent jab. I practice those basic strikes over and over and each time I come back to them, I find some small thing I'm doing wrong.
With these simple tools, sharpened to a keen edge, the martial artist can do amazing things. That is what most people miss. What we remember are the stunning, impossible moves that end the fight. We forget that what got the fighter there, most of the time, were basic moves, drilled continuously. Simple footwork, clean form. If you've been training for less than ten years, that is where I suggest you focus your training. Still, leave room for the spinning elbows and flying knees. They look really cool.