TURIN's scenario rings very true to me. Yet, until I retired from A320s years ago, I led a comparitively sheltered existence - enjoying longer scheduled turnrounds than the budget carriers, and a mangement that tolerated safety as a higher priority than punctuality.
In the early days, we had only CFMs. As a specialist line-checker, one of my concerns when observing external checks was to confirm that the cowling latches were properly observed as being flush with the nacelle. This can only be done by stooping low, and using a torch at night. my reports often reminded crews that the unlatched fan cowlings hang very low and close.
However short the turnround, the flight crew should check them after any engineering work - even if it's just a routine change of the chip-detectors. If that involves a pilot leaving the cockpit after the last of the pax have boarded, it's not going to delay departure more than 5 minutes at the most on an A319. And no engineer worth his salt would be offended by the flight crew completing a check that is one of its listed responsibilities.