The need for covariates—or nuisance variables—in statistical analyses is twofold. The first reason is purely statistical and the second reason is academic.
First, the use of covariates is often necessary when the variable(s) of interest in a study may be connected to, and affected by, some satellite variables (Bottini et al., 2022; Elze et al., 2017; Sassenhagen & Alday, 2016). This complex scenario is the most common one due to the multivariate, dynamic, interactive nature of the real world.