Alias analysis is a fundamental compiler analysis that powers numerous optimizations. While research has focused on deriving more precise alias information assuming that the compiler will optimize better, recent work shows a negligible, or even negative, performance impact of alias information. In this work, we shift the perspective from refining to \textit{relaxing} alias information, \emph{i.e.}, removing information, to complement existing work and challenge that assumption systematically. Our study on a state-of-the-art compiler, LLVM, running the SPEC CPU 2017 benchmark suite, shows (1) \emph{a small overall impact}—removing alias analysis entirely has little impact on the final binaries, (2) \emph{few influential queries}—only a small fraction, namely $\sim$3%, of the alias information leads to changes in the final binary, and (3) \emph{lost potential}—random relaxations can reduce execution time by 21% and binary size by 39% for certain cases, suggesting that compilers could better utilize alias information. Through this work, we advocate that it is beneficial for future research to avoid simply refining the general precision of alias analysis, but also to explore how to find and refine the most relevant queries, and how to more effectively utilize alias information.