Not only do blister packs save so much waiting time — you never have to wait for it unless it's out of stock — but it also feels like there's less chance for anything to go wrong when manually handled by the pharmacist, factoring cross-contamination or incorrect filling, even though the pharmacists would either way be liable for it.
Blister packs are verifiably sealed by the manufacturer, you're more likely to tell if they've been tampered with, you don't have to worry about moisture seeping into the excipient and interacting with the active ingredients, and they provide a visual representation of how many pills you have already taken, without needing to count pills in a bottle.