Not necessarily with Elb design. That is just the design that I have made the most tri lams from, also made plenty of tri lam flatbows too. Hickory or boo backed, tropical hardwood core(or walnut), lemonwood, or bulletwood belly.
I have never made boo back and natural boo on the belly. I have made some with boo floorboard for the belly. They were really pleasant to shoot, but don't contain maximum power fibers like you get with natural boo, with the rind and nodes intact, on the belly. Therefore the limb width was wider, to counter set. You can make a narrower bow with natural boo on the belly, because the material is denser, and you can heat temper it to increase the resistance to compression.
The core for the type of bow you want, I suspect the pre tiller taper is more important than the type of wood you chose.