Recent femtosecond-resolved spectroscopy experiments demonstrate the single-water orientational dynamics in the first solvation shell around monatomic ions to be slowed down. In contrast, dielectric spectroscopy experiments exhibit a blue shift of the water dielectric relaxation time with rising salt concentration, indicative of faster water dynamics. Using molecular dynamics simulations employing nonpolarizable and thermodynamically optimized ion force fields, we reproduce both experimental trends and resolve these conflicting experimental findings by the simultaneous analysis of single-water and collective-water dynamics in the ion solvation shells. While the single-molecule reorientational dynamics of first solvation shell water around ions indeed slows down, the collective dynamics, which furnishes the dominant contribution to the dielectric response, accelerates. This collective acceleration is rationalized by a dramatically decreasing water cooperativity around ions when compared to bulk water, quantified by the Kirkwood dielectric enhancement factor. The static dielectric decrement of salt solutions is thus reinterpreted as a dielectric structure breaking rather than a water alignment effect. Both the dielectric blue shift and the dielectric decrement become stronger with increasing anion size, meaning larger halide ions such as iodide are more efficient dielectric structure breakers than small halide ions such as fluoride.