The problem is, what would you do as a two men crew on a 2 hrs flight if you are notified by ATC that you "probably have lost some parts" (not yet identified at that time) with no indication of a problem in the cockpit.
How likely would it be to be able to identify the damage from the cockpit or cabin (if you leave the cockpit)? How important would it be to have the full flight crew in the cockpit if indeed an issue develops? What would you expect your cabin crew to be able to detect if you ask them to check the aircrafts integrity?
Our actions must start from evidence to be effective. There must be ground staff which asap can identify debris. There must be a way to immediately assess those items (wrt. consequences to the aircraft and looming risk), there must be a way to immediately inform (and not just confuse...) the crew.
Otherwise there (generally) is not much you can do, except for continuing the flight and hoping for the best (or hoping for the designers to have done a good job to make the aircraft damage/falult tolerant).
So what we need, are experienced people on duty, just in case you may need them. At the airport, at the Operators, at the manufacturer, in the cabin. People you can call 24/7 and get an immediate educated answer. Something the beancounters do not like at all.