I am not familiar with AISC & AASHTO specifically, but most codes that I have dealt with have a similar provision. However, my understanding is a little different to Lutfi's. The maximum allowable bending stress in a beam assumes that the beam is restrained against lateral torsional buckling etc. For slender beams, the allowable bending stress will be a lot lower.
When a typical I-beam or Channel section (or similar) reaches first yield in the flange, you are quite close to the full plastic moment capacity of the section. This is because a large part of the total moment-carrying capacity is provided by the flanges, and only a small part by the web. Once the flanges start to yield, you have just about reached the section's ultimate capacity.
Specifically, if you check the ratio of Elastic Moment Capacity (i.e. moment at first yield) to Plastic Moment Capacity (i.e. ultimate moment at which a plastic hinge is fully formed) for typical I-beams, you will see the full plastic moment capacity is only about 15% higher than the moment at first yield. (The actual ratio varies according to the geometry of the cross-section, but usually falls in the range of approximately 10% to 20%.)
However, for a flat plate, the moment at full yield is actually 50% higher than the moment at first yield. This is because the full depth of the plate contributes to the moment resistance, not just the top and bottom surfaces of the plate.
Accordingly, it makes sense to allow a higher bending stress in flat plate than in a typical rolled beam, as this will provide a comparable factor of safety on collapse by bending stress.
Hope this helps!