Just my opinion, but I would want the manager running the show, not the players. After all the manager is the one who gets the sack if the team isn't performing. The players carry on to collect their pay cheques week in week out no matter what.
We don't know that Poch has a zero tolerance approach. I'm sure that when he arrived everyone had a clean slate and started at zero. Maybe over the season things happened where it is now deemed that Lennon has no future at the club, so there's no point him training with the squad. I don't know if you've ever coached or played within a team, but having someone training, who has no desire or motivation really brings down the whole squad. Especially if it's a senior player. No matter how great a player is, he's got to know that he's not bigger than the team. You can't send Ronaldo or Messi out to play by themselves, they need the other 10 players to play for them, so I doubt they would show up to training and not give a shit.
And finally, if Kane did happen to show up to training drunk or anything like that, damn right I'd want to see a zero tolerance approach. He as achieved nothing yet, and he certainly won't win us any titles by himself. There's always 11 players on the pitch and they all have to perform to their very best for us to win anything.