For weight constrained beam applications, both bending and compression failures are bending related (tension isn't).
Since bending strength is proportional to the cube of thickness of a beam, wouldn't less dense materials in practice always win out since you can make the beam thicker?
Ie the characteristic metric for beams would be stiffness / density^3
That qualification of weight constraint. Brick pillars have sufficient compressive strength to hold fantastic weight, steel or stone as much if not more so (the structural rigidity of the bricks will largely depend on the mortar and skill of laying the courses) so I think this is a peculiar niche to be in. Church roofs use heavy trusses, the compression load is a big part of building strength in flying buttresses and arches.
You don’t need buttresses for trusses. A regular horizontal masonry wall will hold and transfer horizontal load just fine. Buttresses are for supporting lateral loads, created by the arches. Brick walls are bad at resisting lateral walls, which makes them them tip over, hence the buttress. Big wood trusses are more recent invention than arches, and they allowed to do away with buttresses.
Good points but the key observation is to weight: wooden beam weight is not often a significant factor in the design of wooden truss roofs, compared to the strength.
Since bending strength is proportional to the cube of thickness of a beam, wouldn't less dense materials in practice always win out since you can make the beam thicker?
Ie the characteristic metric for beams would be stiffness / density^3