You say all this, and I don't completely disagree, but you have coaches who are targeted by the press/media who effectively instigate the beginning of the end. Maybe the coach is sending out these players every game and the players just aren't doing what has been practiced all week. That's not the coaches fault. This is where we've been since Poch and it's because we still have the same blundering idiots making mistakes.
Even a saint, after being bad mouthed in the papers every day for a month is eventually gonna say "It's not my fault Dier doesn't know how to tackle and Lloris keeps throwing the ball in his own net"
Or "If I got the players I needed, like a quality CB or 2, then maybe the rest of the team could play nicer football"
The manager is ultimately responsible for performance of the people they manage. And if, as you say, some players are continually failing to perform in the way they've been coached and instructed, then the manager is failing to get a performance out of said players and needs to take action.
That may mean dropping a player, talking to/bollocking/supporting them, selling them or all of the above. In most cases it's lack of effort that grinds most managers gears rather than a drop in form or confidence. And a good manager knows that different people react to different stimuli, understands their players and knows how to get the best out of them.
Conte came in, set out his standards, assessed the players and decided he didn't want some of them. And I suspect this was mainly around effort/attitude issues. He did it quickly and will continue to do it, it sets an expectation for the group and it helps to create a healthy environment that everyone is putting in the effort. No toxicity, no shit in the press, you keep it in house and cut the negative elements out quickly.
Poch did the same when he came in. Set out his standards, gave everyone a chance and then got rid of the players who weren't pulling their weight, sidelining some of them completely until they could be sold. Not continually trying to cajole people who weren't onside to put in the effort - it's a waste of time, degrades standards and allows resentment within the group to arise (why's that lazy, late fuck playing instead of me, why should I bother if he isn't?).
If I'm continually half arsing it in work, turning up late, missing meetings and deadlines, churning out poor work with a poor attitude then it's up to my manager to address that. And that isn't trying to call me out and humiliate me in front of others. It's sitting me down, finding out what the problem is, telling me how I need to improve and giving me a clear outline of what will happen if I don't and then enforcing that. It's how you maintain a professional environment with high standards. It's good for morale, promotes hard work as the minimum standard and is fair and consistent.
Going public creates a atmosphere of mistrust and fear, it doesn't foster togetherness and once you go public you then allow everyone else to do the same. It's toxic and ultimately destroys any feeling of a team being together and united. You build a team through trust and respect, going public is the antithesis of this.
As an aside I thought the Poch book that came out while he was still manager was one of the biggest mistakes he made, it could improve nothing and only cause harm for the reasons I cite above. I think his ego got the better of him as things progressed at Spurs. It's often the way after you've been somewhere a long time.