We present a large forward-modeling analysis for 55 late-T (T7-T9) dwarfs, using low-resolution ($Rapprox150$) near-infrared spectra and cloudless Sonora-Bobcat model atmospheres. We derive the objects effective temperatures, surface gravities, metallicities, radii, masses, and luminosities using our newly developed Bayesian framework, and use the resulting population properties to test the model atmospheres. We find (1) our objects fitted metallicities are 0.3-0.4 dex lower than those of nearby stars; (2) their ages derived from spectroscopic parameters are implausibly young; (3) their fitted temperatures show a similar spread as empirical temperature scales at a given spectral type but are $sim100$ K hotter for $geqslant$T8 dwarfs; and (4) their spectroscopically inferred masses are unphysically small. These results suggest the Sonora-Bobcat assumptions of cloudless and chemical-equilibrium atmospheres do not adequately reproduce late-T dwarf spectra. We also find a gravity- and a metallicity-dependence of temperatures. Combining the resulting parameter posteriors of our sample, we quantify the degeneracy between surface gravity and metallicity such that an increase in $Z$ combined with a $3.4times$ increase in $log{g}$ results in a spectrum that has similar fitted parameters. We note the systematic difference between our 1.0-2.5 $mu$m spectra and the Sonora-Bobcat models is $approx$2-4% of the objects peak $J$-band fluxes, implying modeling systematics will exceed measurement uncertainties when analyzing data with $J$-band S/N $gtrsim50$. Using our large sample, we examine the fitting residuals as a function of wavelength and atmospheric properties to discern how to improve the models. Our work constitutes the largest analysis of brown dwarf spectra using multi-metallicity models and the most systematic examination of ultracool model atmospheres to date.
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