Climber here… and a big one at that. I’m 6’6", but weigh 178lbs. I have super long femurs which gives me the “long lever” and so I can still put out a high w/kg ratio. I can average 11mph on HC grade climbs that are 6% average.
Speaking from experience, I’ve never gotten faster on climbs when I spend lots of time actually climbing (in fact… when I do that, I usually regress). I live in Tucson, and so one of the benchmark climbs for a good rider here is how fast you can do the Mt. Lemmon HC segment. I got 1:46:XX on the climb this April, averaging 11.8mph. But, leading up the ride, I was hardly doing any training on the mountain at all. Most of time was spend doing super hard, eye-watering, workouts on TR. Most of them were in the VO2 Max or threshold range. Spent a lot time doing TH workouts, with surges above TH. Then when I did the ride itself, I was taking in 400 calories per hour. (I’m blessed with an iron stomach… my wife calls it a nuclear reaction chamber.)