If anyone is willing to help educate a neophyte: from a mathematical perspective, why isn't group-level analysis done in a single step?

As I understand 3dDeconvolve, PSC is modeled in terms of 1) nuisance variables (like head motion, scanner drift, etc calculated on a by-run basis) and 2) regressors for each condition of interest (e.g., a gamma function convolved with stim times). The coefficients associated with (2) can then be put into a group-level analysis where subjects are modeled as a random factor (e.g., in 3dANOVA2).

My question: why aren't subjects modeled as a random effect at the 3dDeconvolve stage? It seems to me that the results would be similar, but that more information would be preserved (as opposed to throwing out all of the within-subject variability, as we do when reducing each subject's data to a single beta parameter).

Thanks in advance to anyone willing to help me think through this.