It is not just the training.
It is not just the gearing.
It is not just the bike's weight, materials and geometry.
It is not just the rider's weight.
It is not just the rider's power output.
It is not just the rider's technique.

It is how all of these and probably several other factors work together and against each other to determine how a bike and rider will climb.

I recently lost 40 lbs. Riding the same bike with the same gearing up the same hills using the same techniques as before the weight loss you would expect that I would climb faster now, but I am actually slower. Why? Because I have not yet recovered my strength (power output). But I am stronger and faster than I was a few weeks ago. As I gain more strength, I will get faster. Eventually I expect to get significantly faster than I was before, assuming I do not regain too much of the weight. The more I work on my conditioning, the faster I'll get. If I also develop better technique, I'll get faster still. If I buy a new bike with a lighter and more rigid frame, I expect I will get even faster.

It would be a rare individual who has maxed out every one of these factors and could not improve his/her climbing.