The whole point of titanium is toughness combined with light weight, for a hellacious price. From that standpoint I would not want to add copper to the utensil. Your statement that water takes longer to boil in a titanium vessel surprises me a bit. I have not noticed noticeably longer boiling times in using my titanium vessels (two), both of which I typically use with somewhat less robust heat sources - Esbit tabs or alcohol rather than a canister or white gas stove.

I can understand that titanium has inherently less heat conductivity that stainless steel or aluminum, but it is typically fabricated in thin gauge material, the better to attract gram counting weight weenies like myself.

My preference for the perfect billy can would be an aluminum container that would nest over a nalgene/gatorade bottle. This would as light as titanium, much cheaper, and functionally as durable, albeit somewhat more prone to denting. Stainless steel is needlessly heavy for most backpacking/climbing applications, but is great where weight is not an important consideration.

I have used aluminum cook sets a lot and I did manage to induce pitting in one pot that rendered it useless. It only took thirty-five years of fairly constant use.

My very favorite cook set is a surplus U S Army Mountain cook set, dated 1951. Two aluminum four liter pots, with a closely fitting stainless steel fry pan/lid. Its only failing is that it is simply too large for most of the trips I do these days. It hasn't pitted yet.
Geezer in Chief