FOQA (the FAA term, Flight Operational Quality Assurance) does what you describe:
Flight Operational Quality Assurance (FOQA)
FOQA collects and analyzes digital flight data generated during normal line operations. FOQA programs provide greater insight into the total flight operations environment. FOQA data is unique because it can provide objective information that is not available through other methods. The information and insights provided by FOQA can improve safety by significantly enhancing training effectiveness, operational procedures, maintenance and engineering procedures, and air traffic control procedures.
Others refer to such programmes as "Flight Data Monitoring".
Right now I believe these programmes are technically voluntary, though if memory serves there is some point where they'll be mandatory. And any carrier operating under a "Safety Management System" (SMS) may find a FOQA/FDM programme a mandatory part of such a system.
Bear in mind, though, that identify a problem is one thing; devising a solution is something else, and forcing its implementation something else again. Note that OEMs have no legal means to impose design changes on operators; only national airworthiness authorities can do that.