Re: "... anti-stall – sorry, plane pedants hate it when we call it that..."
"Indeed, many fighter planes are also unstable."
This is very much the difference. Civil transport aircraft aren't supposed to BE dynamically unstable under any reasonable circumstances(*), let alone need software/hardware to correct it, or special recovery procedures.
The largest 737NG was _ALREADY_ dynamically unstable (ever increasing stall characteristics) and as such should have been the absolute end of the line.
(*) Deep stalling of a T-tail is an extreme condition well beyond any kind of normal flying - on civil transports usually only ever encountered in extreme handling tests.