Why are melody and rhythm difficult to separate in musical performance?

Melody and rhythm are difficult to separate in musical performance because music is fundamentally a temporal art, and rhythm serves as the indispensable "order in musical time" that organizes all other elements.12

While rhythm can exist independently of melody—such as in percussion-based music—melody cannot exist without rhythm. A melody is defined as a linear sequence of tones perceived as a coherent line, but this sequence is inherently an aesthetic product of pitches arranged in time. Rhythm provides the necessary durational substructure that gives a melody its phrasing, motion, and structural cohesion.1324

In practice, rhythmic identity is what endows pitch relationships with specific characteristics, allowing listeners to perceive a series of tones as a unified musical idea. Because rhythm determines the timing and duration of every note within a melodic line, the two elements are inextricably linked; the rhythmic structure dictates the flow and tension of the melody, making them inseparable components of a single musical experience.214