My first rifle build was a full stock long rifle that I built with a piece of lumber that I bought in Brazil. I don't know the species, which was not an issue at the time. I bought it because it was pretty, big enough, and had very straight grain, which was important since I was not going to use power tools.
I was working on a ship that went down the East coast of SA regularly, so I could bring back whatever I wanted to. I brought back what seemed at the time to be a lot of wood, but I wish I had brought ten times as much.
That was, I guess, 1986. I built it for my Dad, but it is mine now, and my favorite ML rifle. The wood is much darker than walnut, fairly heavy, and waxy enough that it polishes up nicely without needing an applied finish. Probably some type of rosewood.
The rifle I am referring to is pretty heavy, but it with a very long barrel, it was going to be so even if the stock was spruce. In fact, to get the balance point where I wanted it, the butt plate is 1/4" bronze.
Some of those exotic woods are sort of brittle, most are quite heavy, and as others here have mentioned, the dust can sometimes be very nasty.