  The charge density wave (CDW) or nematicity has been found to coexist with
superconductivity in many systems. It is thus interesting that the
superconducting transition temperature $T_c$ in the doped BaNi$_2$As$_2$ 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$_{1-x}$Sr$_x$Ni$_2$As$_2$ 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
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 $T_c$
in this system should be understood as the six-fold suppression of
superconductivity in undoped compounds.
