We have steels and 'right now' technology to build ultra light shotgun barrels without the need for titanium.
As chuck notes, some of the processes we can work our steels aren't cross-functional to titanium alloys.

Replacing receiver material with aluminum or titanium never made so much sense to me -- in that especially with a double, the 'magic' in the handling comes from keeping the guns slender, slinky, and with the weight between the hands.
The receiver is metal between the hands.

I think the reason then to Steve's 'why...' is that we 'have it' already with high tech barrel steels, slender designs, and long boring bits to balance things from the stock end -- without the unnecessary cost of processing highly exotic materials.


--Tinker