The charge density wave (CDW) or nematicity has been found to coexist with superconductivity in many systems. Thus, it is interesting that the superconducting transition temperature Tc in the doped BaNi₂As₂ system can be enhanced up to six times as the CDW or nematicity in the undoped compound is suppressed. Here we show that the transverse acoustic phonons of Ba_1−xSr_xNi₂As₂ are strongly damped in a wide doping range and over the whole Q range, which excludes its origin from either CDW or nematicity. The damping of TA phonons can be understood as large electron-phonon coupling and possible strong hybridization between acoustic and optical phonons as shown by the first-principle calculations. The superconductivity can be quantitatively reproduced by the change of the electron-phonon coupling constant calculated by the McMillan equation in the BCS framework, which suggests that no quantum fluctuations of any order is needed to promote the superconductivity. On the contrary, the change of Tc in this system should be understood as the sixfold suppression of superconductivity in undoped compounds.