In the first world, brick construction is extremely expensive and you're right -- modern residences are often built with structural beams (whether wood or steel), and the brick is usually just a veneer.
But in the third world, variants of brick (e.g. cinder block) are often the norm, and are structurally load-bearing, and work fine for two to three stories. And they're very easy and cheap to build with.
The US has a ton of cheap lumber so load-bearing wood frames are common. Many countries don't have forests like that so bricks/blocks are the way to go.