Over the last few decades, evolutionary population synthesis models have powered an unmatched leap forward in our understanding of galaxies. From dating the age of the first galaxies in the Universe to providing detailed measurements of the chemical composition of nearby galaxies, the success of this approach built upon simple stellar population (SSP) spectro-photometric models is unquestionable. However, the internal constraints inherent to the construction of SSP models can hinder our ability to analyze the integrated spectra of galaxies in situations where the SSP assumption does not sufficiently hold. Thus, here we revisit the possibilities of fitting galaxy spectra as a linear combination of stellar templates without assuming any a priori knowledge on stellar evolution. We showcase the sensitivity of this alternative approach to changes in the stellar population properties, in particular the direct connection to variations in the stellar initial mass function, as well as its advantages when dealing with noncanonical integrated populations and semi-resolved observations. Furthermore, our analysis demonstrates that the absorption spectra of galaxies can be used to independently constrain stellar evolution theory beyond the limited conditions of the solar neighborhood.