Why? Ti is very strong and very light. Theoretically you could make bars much lighter than aluminium by making them thinner. Still as strong or stronger but deflection is independent of material strength and only dependent on section size so if it is thinner it will flex more. If the thickness is the same as aluminium the flex will be the same and the bars still lighter but material properties are such that it transmits more vibration. This I am guessing since I dont have solid data just my observations but it is possible due to the stronger material properties. My Muru Ti frame is very light and thin and it is flexy.
Sort of but not quite. Different materials have different inherent properties and behave in different ways. Aluminium in its pure elemental form is light, but not exceptionally strong, not particularly stiff, nor very springy, and has a particular dislike for repeated flex cycles, weakening every time it bends. Therefore it is alloyed with various other elements to improve particular characteristics, but it still has a fundamental dislike for cyclic stress, so stiffness is often a focus for durability, sometimes at the expense of comfort.
Titanium is heavier than aluminium, a lot stronger, very springy, but still not especially stiff. The inherent strength means a titanium part can be built down to a similar or even lighter weight than the aluminium equivalent, however rigidity suffers (more) so you lose some effiency of input. The superior springiness does soften the bigger bumps, but does little over the fine stuff.
I've ridden Ti frames, and they're bloody nice (one also had a Ti fork, that was ..... er..... interesting to put it mildly!). Would I choose it for a handlebar? No.