We argue that recent measurements on both the superfluid density and the optical conductivity of high-quality LSCO films can be understood almost entirely within the theory of disordered BCS d-wave superconductors. The large scattering rates deduced from experiments are shown to arise predominantly from weak scatterers, probably the Sr dopants out of the CuO$_2$ plane, and correspond to significant suppression of $T_c$ relative to a pure reference state with the same doping. Our results confirm the conventional viewpoint that the overdoped side of the cuprate phase diagram can be viewed as approaching the BCS weak-coupling description of the superconducting state, with significant many-body renormalization of the plasma frequency. They suggest that, while some of the decrease in $T_c$ with overdoping may be due to weakening of the pairing, disorder plays an essential role.
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