Juan Mata is 30. He's gonna be 31 this season, and he never was a physical specimen. He's not a top player anymore, Jose or not. Sanchez is 30 in days and has more miles on his tires than a 92 Honda Accord. There's an argument to say that both are past it, with Sanchez having astronomical wages. You also have to cater your side to help their abilities. I don't think Pep does that. Herrera with a better manager might make improvements, but that's not a guarantee. Martial is a talent, but it's always been about potential more so than his actual performance. He needs a move more than he needs a new manager.
But once again, you're ignoring their severe problem that I've stated over and over that would prevent most managers from getting them higher up the table. Sure, they need to score goals, and much of their offensive players aren't. But their backline is trash. None of that backline is worth much of anything. They've let in 29 goals. That's borderline criminal for a team who is supposed to get in to the top 4. Certainly, Pep might be able to improve it some, but it's not like Jose isn't know for playing defensively. He's got 8-9 behind the ball and they still can't stop it.