My overall question is: why use bayesglm instead of other classification methods?
Note:
I feel like the sample size is large enough the parameters of a regular logistic regression are going to be normally distributed (CLT). What would I gain by specifying priors? My hunch is that it will only matter for a small dataset, but I don't have any theoretical or applied evidence.
In engineering, as well as supply chain risk management, "engineering knowledge" --eg an educated persons best guess-- may be the best data you have. For example, the likelihood of a tsunami occurring and disrupting the supply chain, without additional data, can be estimated by an expert in the subject (there are better methods for constructing priors). As time passes, tsunamis occur and, as a result, we gain more data, and can update our priors (engineering knowledge) with posteriors (priors adjusted for new data). At some point, there will be so much data that the initial prior is irrelevant, and no matter whom made the prediction, you will have equal predictions of likelihood.
It is my belief that if you have that much data, a "traditional" Frequentist approach is (typically) preferable to the Bayesian approach (of course others will disagree, especially with choosing between statistical philosophies rather than sticking to one and selecting an appropriate method). Note that it is entirely possible (and occurs often) that the Frequentist approach yields similar/identical results to the Bayesian.
That said, when the difference in methods is a line of code, why not implement multiple methods and compare the results yourself?
