Why don’t we provide top bars from one-third of a slab
Generally, we provide rebars to counteract the tensile stresses (apart from temperature bars). In slabs or beams, for service loads (i.e. gravity loads), the slab is deflected in sagging curvature. It means that the bottom face of the beam/slab is stretched (in tension) whereas the top face is compressed in the mid region. But due to the rigid connection at the ends of the members, just the opposite stress occurs. Tension on top face and compression on the bottom face. (See BENDING MOMENT diagram of any beam/slab under gravity loads)
Concrete itself is good in resisting compression. Hence to economize the structural element, we usually do not need top bars at the top in the mid-span (middle one-third) of beams and slabs but is required by design at the ends.