From a business point of view, you are correct. Dyche has been paid about £5.5m for his half-season, in which we stayed in a league worth at least £120m tv money alone.
As for 'perilous position', I largely agree, but it's still somewhat debateable. Yes we had blown golden opportunites under Frank and kept him far too long, but the fact still remains: Dyche had 18 games to overturn a 1 point deficit with a better goal difference if I recall. He achieved his remit with half an hour of the season to go, but for me it is not the miracle or mission impossible some people make it out to be.