The reason this is so, is because of the physics of the instrument itself. It has a richness harmonically not present in the sounds generated by any other instrument. The other closest examples would be the harpsichord and piano, in terms of modern instruments, but they have a quite distinct and different tonality, and that is a part of the difference here that makes the harp special. There is a particular richness in the overtones because of the gentle quality of the overall sound, that the overtones are a more discernable component than in the case of the other string instruments via keyboard percussion, and the fact they are somewhat muffled in being housed within a wooden cabinet.
It is that interplay of the harmonics that acts as a kind of tuning fork for the soul. It is the soul that yearns for alignment, and music serves the soul by providing a vibrational equivalent to what it is yearning for. It can be a mirror of the soul and lesser, more disconnected, levels of the being as well, depending on the origin of the music and how it is expressed and becomes detectable. The harp is particularly satisfying because it is the most in tune with the soul of any other sonic equivalent. The human voice is compelling as much for the fact it is music generated from a living being with a heart and mind and a soul driving the physical extension and, as such, adds greater overlay of intuitive force to convey meaning in what is being sung. But a voice alone only has a narrow range of vibration in what can be conveyed from moment to moment, compared to the many strings of the harp that can be sounded almost simultaneously, creating quite a cascade of sonic delights and harmonic resonance.