So the assumption is that taking training and therefore increasing our competence as riders increases our speed?
Not so sure about this.....Maybe for some, but I feel that training teaches us how to focus our attention on the things that matter, ignore the things that don't and be able to handle that information accordingly.
Track training, trackdays and racing teach us how the bike will behave at it (or our) limits, and shows us that 9/10 times it's us and our actions that's the limiting factor (Weeksy's the exception, cos he rides a Gixxer

and is therefore severely limited by the bike

Gonna get my ass kicked at Brands now....)
Road training teaches us all about hazard perception and how to deal with these things, and place ourselves in situations as far from these as possible whilst still making progress safely.
At the end of the day it comes down to mental state, and how we choose to approach riding in each of these environments. The road is no place for flat out riding 100% of the time, and the tracks no place for taking the scenic route (except at Oulton). If we choose to take the skills we learn on the track and ride to our limits on the road, we will get hurt, and may take others with us, but, if we back off, and use all the extra attention we now have to focus on hazards, we become safer, smoother, and a lot more relaxed.
Do track training, combined with road training and I believe we'll become more rounded riders, Chris Walker still rides on the road, as does Rossi, if it's good enough for them, it's good enough for me.
I think I'll lay off the caffeine for a day or two.....