Allegri's main attribute was his winning mentality IMO. He made the players believe. Remember that almost comeback in Madrid? That could not have come with tactics alone. Sometimes Allegri does have a negative mindset but I'm sure he'll eventually learn from it.
He already did imo. That 2017-18 season, after the Cardiff second half collapse with the knocks to Pjanic and Mandzukic, we absolutely smashed the league. Record goal differential and most goals scored in the modern era. 86 goals scored-24 goals conceded. Our average win that season was by 2+ goals. We won 30 matches in which we scored 80 goals and conceded 15. That’s dominant, goalscoring football.
We also put 4 goals past Spurs in the two matches, where the tactics were super defensive and cynical, counterattacking football, but perfect for against a younger, more athletic, hard pressing team, and we easily could have scored 8 goals over the 2 leagues, with a missed penalty, a clear penalty not given for a foul on Costa, and multiple great chances missed. And after the disaster first leg against Madrid, in which Buffon-Chiellini screwup plus Dybala red card played a big part, we put 3 past them at the Bernabeu and only got knocked out on controversial last second penalty.
Smashed AC Milan in the Coppa final 4-0 too.
If we had upgraded the aging and declining midfield after that season, we are probably in a much better place right now.