Too often riders with excessive power race from corner to corner only to gently bend the bike around the next turn and then turn the dial to eleven before wildly backing off and carefully making the next turn.
I think it's wrong to confuse rider error with bike selection. Rider error can take place on the straights on a liter bike but it can also take place in the corners of a low power bike. A rider can ride too fast regardless of where he/she is or what he/she is riding.
My first bike was a M696. With only ~2000 miles on it, I signed up for the Keith Code school and got a chance to ride the S1000RR. Though I was hugely intimidated, the first thing I noticed was how much easier to ride the BMW was in every single way. I cornered way faster on it than I ever had the courage to on my Monster. And while a part of me hoped that my new found "skills" would translate to the Monster when I got back home, they didn't. I always found the Monster tricky to ride until the day I sold it.
But my point is that I only enjoyed the BMW because I exercised a lot of self control. I never got over 10k rpm so I was only experiencing 848-like power. I sat up between the corners and maintained a speed that would make braking and corner entry stress free so I could concentrate on cornering. And I did get better, smoother, and more confident. My body position, bar inputs, and throttle control were all improved. In short, the time I spent on that high HP beast of a bike made me a better rider.
That said, I want an Aprilia 125 for the track. I know it's no longer available in the US. I'm just saying I want it. It's fast enough for me. It's cheap. And I bet it's a real hoot. I just wanted to point that you can buy a liter bike and still approach rider education with the right attitude and still develop. Every liter bike in the world makes 35 bhp if that's what the right hand asks it to make.