The following passage about the merits of density-functional perturbation theory (DFPT) is extracted from this seminal paper: Phonons and related crystal properties from density-functional perturbation theory
One of the greatest advantages of DFPT—as compared to other nonperturbative methods for calculating the vibrational properties of crystalline solids (such as the frozen-phonon or molecular-dynamics spectral analysis methods)—is that within DFPT the responses to perturbations of different wavelengths are decoupled. This feature allows one to calculate phonon frequencies at arbitrary wave vectors $\vec{q}$ avoiding the use of supercells and with a workload that is essentially independent of the phonon wavelength.
Phonopy is an open-source package for phonon calculations at harmonic and quasi-harmonic levels. In particular, Phonopy is interfaced with VASP. The following link is the tutorial about how to calculate the phonon band structure of NaCl with VASP+DFPT.
However, the second step of this tutorial to use VASP is the construction of a supercell. Why?