Hi Justin,
A bamboo shafted ice ax, I think that's a terrific idea! I, too, made alpenstocks for myself and friends when living in the PNW, where bamboo, having gone over the wall from backyard gardens, now grows wild in certain city parks and vacant lots and is free for the taking. And you're right, it's super strong, light, resilient, and can be easily field repaired.
Back in the day, all x-country ski poles were bamboo. Why? Because they are strong, light, resilient, and can be field repaired. It's very hard to break bamboo; when stressed it tends to split along the length of the shaft between the joints, unlike CF or alu poles, which can just snap in two. All that is necessary to repair a bamboo pole is a few turns of electrician's or duct tape: voila, fixed! My poles, made in Norway by Liljedahl, the first and only poles I've ever had, much older than the majority of the participants on this site, are still going strong, and only one has a bit of tape wrap. The weight is about 9 oz.
In addition, there are bikes frames now being made of bamboo (and there always have been rims made of rosewood). Ice axe handles, too, once were made of natural materials at one time, until REI put one under several tons of pressure on a hydraulic press and said, "see, they break, so you need to buy one of our new metal shafted ice axes." And so went the way of the industry.
So, yah, I'd like to see a Ti/bamboo snow tool; sign me up!


