If constant factors are significant in practice and the size of the input is not significant, then big O notation is not the right tool for the analysis, and that's perfectly fine. For instance, we generally don't talk about big O notation when comparing the performance of SSDs and spinning HDs.

Big O notation is for describing how the performance of an algorithm changes as the size of its input changes. If the size of the input is not a significant concern, then it's totally fine to not use big O notation for analyzing the problem.