They exist! Meant for backpacking/back country work.
I spent a summer as a wilderness search and rescue intern/volunteer/grunt/mule during college and was shocked at how much weight could have been saved with better gear. There’s just a minimal market for it.
I don’t believe it. Titanium is, mechanically, a great material for a lightweight pot, but in my limited testing, I don’t think it’s inert enough. Green tea in a titanium pot is especially nasty.
My current favorite cooking surface is the coating used on Hestan Nanobond. It’s sold as “titanium” but, from reading the patent, I think it’s a bunch of layers of CrN, TiN, and AlN, applied by PVD in a process optimized to produce an attractive gray color that looks a bit like metallic titanium. It seems very hard, very durable, and does not obviously react with any kind of food. (And even if it did, unless something oxidized the Cr to +6 and made it soluble, nothing that might leach out seems likely to be harmful.)
The patent seems to expire fairly soon, and maybe the process will take off. I wonder if this coating could be applied to a lightweight titanium pot with good results.
[0] Concretely, this means that, when cooking solid food, the parts of the pan where the food isn’t sinking heat adequately get too hot.
https://www.gutenberg.org/ebooks/18137
the audiobook read by Tabithat is just about professional quality and is highly recommended:
Garage Grown Gear has some of the trendy light and ultralight stuff.