Context. Spatially resolved observations of the Sun and the astronomical sample size of stellar bodies are the respective key strengths of solar and stellar observations. However, the large difference in object brightness between the Sun and other stars has led to distinctly different instrumentation and methodologies between the two fields. Aims. We produced and analyzed synthetic full-disk spectra derived from 19 small area field-of-view optical observations of solar flares acquired by the Swedish 1-m Solar Telescope (SST) between 2011 and 2024. These were used to investigate what can and cannot be inferred about physical processes on the Sun from Sun-as-a-star observations. Methods. The recently released Numerical Empirical Sun-as-a-Star Integrator (NESSI) code provides synthetic full-disk integrated spectral line emission based on smaller field-of-view input while accounting for center-to-limb variations and differential rotation. We used this code to generate pseudo-Sun-as-a-star spectra from the SST observations. Results. We show that limited-area solar observations can be extrapolated to represent the full disk accurately in a manner close to what is achievable with Sun-as-a-star telescopes. Additionally, we identify nine spectral features, four of which are caused by instrumental effects. Most notably, we find a relation between the heliocentric angle of flares and the width of the excess emission left by them as well as a source of false positive coronal mass ejections-like signatures, and we defined an energy scaling law based on chromospheric line intensities that shows that the peak flare contrast roughly scales with the square root of the bolometric energy. Conclusions. The presented method of creating pseudo-Sun-as-a-star observations from limited field-of-view solar observations allows for the accurate comparison of solar flare spectra with their stellar counterparts while allowing for the detection of signals at otherwise unachievable noise levels.