The EPL season is one of the toughest league in Europe. The best is always expected from elite teams, more reason we're seeing these managers not having some long span in their managerial role in the club, any average performance trigger, they're sacked. As a matter of fact, to stay fit, you have to be a genius and versatile in every sector.
Clubs in Premier League have changed a lot recent decades with more priorities leaning towards financial benefits. With burden of fighting for income in order to maintain their club financial health, it results in more pressure on head coaches. Bad season means some sort of damages to their club financial balance. Therefore, clubs no longer have similar patience like in the past and head coaches nowadays are more vulnerable to sacking risk.
The Spurs have suffered all these years without setting their eyes on a golden trophy but now, they can relax because they accomplish good results. Tottenham Hotspur ranking close to the bottom zone this season, it does matter but Ange Postecoglou had evidence to show the fans and the management in his second season. There have some up and down movement, the best is definitely going to be called out.
They are not a successful club with no title over many years and this trophy polishes their club history a little bit. Postecoglu is part of this success but in other things he generally did bad management for Totteham Hotspur. Their boss felt unsafe if continuing to cooperate with him next season.