Moyes brought stability. Got us into Europe pretty much season after season and was draining every inch of quality from a group of average players.
Martinez achieved our all time highest PL points total.
Koeman was sacked when the going got tough at the start of his second season.
Moyes second season was 17th and our lowest points tally ever. His first season was 7th achieving nothing. By your criteria Allardyce should have never left.