Why is the term sonata-allegro form sometimes misleading?

The term sonata-allegro form is considered misleading because it implies that the musical structure must be performed at a quick, or allegro, tempo. In practice, this form is not restricted to fast movements; it can also be utilized in slower movements, such as the second movement of a sonata, despite their slower tempo.12

While the designation originated because the first movement of a Classical-era work was typically a serious allegro, the structural pattern—consisting of exposition, development, and recapitulation—is independent of the speed at which the music is played.123