Titanium is a great metal for stopping pistol and rifle rounds. I’ve seen quite a number of videos of people shooting titanium and even the largest rounds don’t make much of a dent, including .50 BMG FMJ. However all the trauma plates that I see available for civilian purchase use AR500 steel. A great bullet stopper for sure, but it isn’t exactly light.
So, why aren’t titanium trauma plates available? Sure it would cost more than steel, but I’m sure there’s a market.
IDK but for backpacking Ti is about 5-10x the cost of steel, while Aluminum is about 1/4 - 1/2 the cost of Titanium. Aluminum and Titanium dominates over steel, but steel still has it’s uses. Al is actually a bit lighter than Ti but needs to be bulkier to be strong enough, thus added weight again. Steal can be thinner than Al and actually is not bad in a weight to strength ratio. Ti is a expensive luxury where you get some of the strength of steel with some of the weight of Al (the saying is the strength of steel with the weight of Aluminum, but that simply is not true - but it is a very happy compromise)
For your purposes I would assume Aluminum would be useless, so it appears the cost difference.
Titanium is softer than steel but lighter; aluminum is softer than titanium but lighter. They make things out of titanium rather than steel because it has to be lighter, plus there’s that “no rust” thing it’s got going for it. Otherwise, as stated above, yeah, it’s heck of expensive (less so since the Soviet Union fell and they’re not using it to make as many aerospace craft).