Why not a titanium body ?

Current camera housings are made by a die casting operation from magnesium alloys. Die casting has a large set-up cost (the die tooling is expensive to make) but it is capable of high precision, surface finish and small feature size. It also has a short cycle time (parts can be ready under a minute) so you can cast parts very quickly reducing cost. The part finish is often good enough for final use with minimal post-processing. However die casting is currently only practical for comparatively low melting point materials (Al, Mg, Zn, Cu). Titanium cannot be typically used in die casting.

To make a camera housing out of titanium (which would not be pure Ti btw but rather an alloy such as Ti-6Al-4V) using a casting process you would need to either use permanent mold casting with the mold made from a refractory ceramic material ($$$), or using investment casting which is slow and labour intensive. Ti is also highly reactive and may need to be cast in an inert atmosphere. All this will increase cost substantially compared to die casting of Mg alloys.

Alternatively you could machine the housing but Ti has poor machinability requiring premium cutting tools and machining is wasteful and slow.

As another alternative you could could also forge/form the housing to near-net shape and then post-machine. This is how the old film camera Titanium special editions were made and how the top housing of the new Fujifilm X-Pro 3 is made. You can see the process in the video below

https://youtu.be/1cvNBULS3tM?t=4099

It requires several tools to progressively shape the top cover (slow compared to die casting) and the resulting part cannot be as complex and detailed as a die cast part. This is why Fuji only makes the top cover out of Ti and not the whole housing, which is still die cast Mg alloy.

The best way to do it would probably be metal injection molding which would be faster and could achieve higher complexity but it is still an emerging manufaturing process for Ti materials and not that widely used.

So as you see Titanium is not easy to work with and will make the camera housing more expensive and more constrained in shape complexity (problem for engineers).

It also has low thermal conductivity which makes it worse than Mg in dissipating heat build up from internal electronics.

The increased strength does not provide much benefit since the internal components are sensitive to shock and will get damaged anyway under any substantial loading.

So why bother using it for a camera? really only as marketing gimmick and fashion statement for the customer. Kind of like the Leica special editions with crocodile leather and artisan camera straps etc.