This team has been in need of some reinforcement for a long time. Allegri wasn't given enough money. But maybe Motta can be given. Then we would find out how good he will do after adding new players.
From what I've seen, Juventus' squad isn't 100% the same as it was during Allegri's time. This means that the new coach has had room to make changes and yet Juventus is still not fighting for the title. When a team doesn't get good results, then it's all the coach's fault, because it's up to the coach to choose the players who will be on the field, define the formations and positions of the players and also choose the new signings.
There is no way they will not make some adjustments between the period Allegri was in charge and now that Thiago Motta is in charge. I don't know about Allegri not being given enough money because I have not read about his complaints of such anywhere in the print media. It is possible but there is no verification for now. So, just like you rightly said, we could see a lot of changes with Thiago Motta in the team, maybe he has more freedom and more resources at his disposal. Actually, a lot of work still need to be done about the club. They are defending well, but their attacking formation is still not that perfect.
Juventus = 22 games, 8 wins, 13 draws, 1 loss, 37 points
Lazio = 22 games, 12 wins, 3 draws, 7 losses, 39 points
With this current coach, Juventus won't be Serie A champion this season or next.
This season you may be right that Juventus will now be champion but for next season, I don't think so. Juventus is a big team and one of the most popular team in the Italian Serie A. They would want to maintain that status and the only way to do that is to win the league title often without giving much gaps. Therefore, next season they might go to market to bring new faces that they will blend into the team to fortify them and target the title which they might eventually win.