There are far more peaking players in Brazil nowadays than a few years ago as the likes of Flamengo and Palmeiras can pay much higher wages, so their squads are fairly stable. But no doubt there is always a risk of Brazil-based players moving during the WC cycle and thus the squad might need to change over time, which would harm results.
But my point is not so much thinking we could win with a Brazil-based squad, I suspect the quarterfinals is more or less (luck, etc aside) the normal 'best' we could do, which is not too different from current results. Since we are going to lose anyway, at least we would have a team that feel Brazilian.
As for the manager, Tite made mistakes like the ones you mentioned, but foreign managers made mistakes too. We have also had many foreign (European and Argentine ones) managers in Brazilian football in recent years and they didn't do much better in general than local managers, so I have doubts that just hiring a foreigner would improve things. We had Paulo Sousa from Portugal as Flamengo manager and he benched Pedro because he didn't know how to play Gabigol and Pedro together...Then Dorival Júnior (Brazilian) came and made them play together.
Obviously a really top one like Guardiola could do very well, but that kind of manager is out of reach. So we would probably end up with some manager from abroad who is not really any better than what we already have here (someone like Paulo Sousa mentioned above).
if I were to choose the new manager of Brazil, I would choose Fernando Diniz from Fluminense.