It's almost the opposite. There is automatic monitoring for stable approach criteria (simplified: you must be at speed X with flaps selected etc by altitude Y). So this example would cause an automatic report from the aircraft to the airline, because they were too fast (not within stable approach criteria) and still continued the approach instead of going around.
However even in those cases it's not meant for punishment but for safety improvement. In most professional operations these reports are made anonymous, and only for example someone from a union committee gets to know who the crew were and could have a talk with them if necessary.
But the cause of a need to go around can be pilot error. There could be non-pilot error needs for a go around like when there is a runway incursion so the pilot is waved off. If a pilot makes a bad approach, would that not be pilot error? Not being a pilot, I'm not sure of the procedure. I'm assuming a 767 uses autopilot for the majority of the flight. I just have no insight on whether the pilot or the autopilot is responsible for the approach.
The industry does not treat a go around like an error. You'll only ever get questions when you don't go around while procedures clearly require it, like what seems to have happened in this case.
On autopilot use: The pilot is always responsible for the approach. You can definitely have an unstable approach on autopilot if you configure it wrong or ask it to do things that can't be done within the stable approach criteria. A common example is trying to slow down and descend at the same time, most jets can't really do that.
But "responsible" does not necessarily mean to blame in aviation. The industry as a whole follows the Just Culture principles (see: https://www.caa.co.uk/general-aviation/general-aviation-at-t... ) The purpose of a report is to learn from it and improve safety, not to blame the crew.
Part 121 Cargo and Part 135 Charter are ... another story. Quality of training and procedures vary a lot. Some are run about as well as the Part 121 Passenger operations. At others a go-around is a career-limiting move.
I do not know how 21Air operated - leave that to the NTSB to discover - but it would not surprise me whatsoever if Amazon leans heavily on their contracted ACMIs and yanks contracts for delays. A go-around means an extra 15 minutes (give or take) and Amazon cuts their logistics schedules razor thin so they don't have to pay for extra labor. A 15-20 minute delay in unloading the airplane can mean the sorting center staff and delivery trucks sit idle (though it wouldn't surprise me if they just stiff the delivery contractors for the wasted time).
This isn't necessarily done with ill intent - the middle managers at Amazon are just chasing their numbers and an operator that prioritizes safety will inevitably have worse on-time performance. As is often the case these days outsourcing / contracting can end up being a race to the bottom even if no one intends it that way. FedEx Ground is all contractors who bid on routes. If you ever wonder why the driver throws your package or leaves it in your driveway: they had to be the lowest bidder to get the contract and that means X deliveries per hour or they lose money. It just so happens that with air cargo operations this kind of pressure can easily lead to an accident.
However, I don't doubt shady operations might be doing this(more so if they aren't carrying passengers). They won't be around for long if they are caught doing this kind of nonsense and it causes an incident (or accident in this case).
Today there may be some rules (more than X go arounds because of weather, you have to divert, etc).
If there is a company willing to bend rules to increase profits, I'd bet it'd be Amazon's retail side. Not via explicit punishment, because that'd be too easy to catch, but bonuses for timely arrivals, fuel efficiency, and so on.
Claiming that this company is making Aviation unsafe is a serious accusation, that requires evidence.
The incentive is to pick the lowest bid and that could be a company whose culture creates indirect pressure on pilots to be on time. All it takes is a dispatcher in a small company that is constantly irritated when things are late. Knowing that the other people are going to be angry with you for being late can make you hesitant to go around, causing exactly this type of accident.
Is this what happened? Probably not. Pilots get tunnel vision for any number of reasons.