Maybe Tuchel would really be better for Bayern Munich in every way. But I still think that attitude against Nagelsmann was unfair. They could have at least waited for the end of the season before making such important decision.
~
I agree with Pulsar77 about the timing. Mid-season isn't the best time to switch the management and players will require some time to get used to the new coach strategy. What might be good, is the international break. The advantage of having a week before the next game rather than 1-2 days is important. There is also 2 weeks to prepare the team before facing City in Champions League.
Otherwise, Bayern players are professionals and I assume they will get used on him fast.
I think sacking can happen at any time and in the world of football I think it's normal to happen and even, Tuchel was sacked by Chelsea very suddenly and Tuchel is still in good condition until now. Also, Tuchel has good experience when he becomes a substitute coach in the middle of the season, even Tuchel can handle a team in a situation where the team is under high pressure.
Maybe this factor is also expected by Bayern Munich, because it looks like Tuchel has the ability to be able to make Bayern Munich have a good dominance again. Also, basically the rumors of Bayern Munich signing Tuchel had already occurred when Tuchel was sacked by Chelsea, but in the end Bayern Munich only made it happen now.