That's the thing. Having one engine shutdown is not a "close call" in a mathematical or engineering sense. The failure rate for revenue service transport category aircraft is well studied. The failure rates are in the 10⁻⁷ to 10⁻⁶ per flight order of magnitude.
In multi-engine turbine transport-category aircraft, an engine shutdown rarely results in a mishap. Extremely rarely. If the goal is safety, shutting down a possibly misbehaving engine is safety enhancing over an alternate system where an engine shutdown results in meaningful fines and so there would be pressure to not shutdown an engine that should be shutdown (or a delay in making the decision to do so).
I'll have to double-check this later, but I think if you took a 50 mile drive to the airport, got on a flight that had an engine failure at V1, and drove 50 miles back to your house that you were at a greater risk during the 100 miles of driving than during that worst-case single-engine shutdown flight. (They're order of magnitude the same I'm pretty sure. If safety is the goal, how much should each of the people who commuted to that flight be fined for their risk-assumption?)
In multi-engine turbine transport-category aircraft, an engine shutdown rarely results in a mishap. Extremely rarely. If the goal is safety, shutting down a possibly misbehaving engine is safety enhancing over an alternate system where an engine shutdown results in meaningful fines and so there would be pressure to not shutdown an engine that should be shutdown (or a delay in making the decision to do so).
I'll have to double-check this later, but I think if you took a 50 mile drive to the airport, got on a flight that had an engine failure at V1, and drove 50 miles back to your house that you were at a greater risk during the 100 miles of driving than during that worst-case single-engine shutdown flight. (They're order of magnitude the same I'm pretty sure. If safety is the goal, how much should each of the people who commuted to that flight be fined for their risk-assumption?)
FAA studies on the topic:
https://www.faa.gov/aircraft/air_cert/design_approvals/engin...
https://www.faa.gov/aircraft/air_cert/design_approvals/engin...