You're right. My broader point on the subject is just that we also don't know what kind of condition the water from the store is in, but we accept that it's 100% problem free without question. We don't know what that facility (or the total supply chain) look like either.
I do think/believe/suspect that the bagged ice is less sanitary than bottled water or RO out of the filter at the grocery store. However, I also think that the actual difference is very small and that if there is a statistically significant difference, it's not enough to impact the brewing process. A significant difference does not mean it changes the result.
Many of the practices that we've adopted as safe and normal are simply dogma. For the homebrewer, perfection is not the elimination of all risk - it's achieving a desirable result.
My anecdotal evidence through a dozen or so batches is that it's not causing infections. It is accelerating my brew day tremendously at a very very low cost. The cost of a really nice wort chiller will never be as low as bagged ice, even over many batches. Thus, I view this as a legitimate practice that should be shared.
EDIT: Sorry - To your first point, one of the great things about the bagged ice is the high surface area. It makes it super fast. But if someone wanted a safer option and cared less about a good cold break, then a clean block of ice would be a good option. I appreciate you bringing it up.