It wasn't supposed to show in theaters until October 2021 (which meant not on Disney+ until roughly March 2022) and clearly it's ready now. They were holding it so that the shows could continue making money and by October 2021, most of the tours were going to be coming to an end anyway. Right now there's no start date in sight for Broadway, West End or any Touring productions, so this is the optimal time to bring Hamilton home. This will help tide over fans who maybe had tickets to see the show and will be a fun thing for fans who never got to see the OBC or maybe just has never seen the show period.
There has always been a worry (from the money people; Lin has been talking about this since 2016-ish) about giving the show to people in their homes though since it still commands such high ticket prices. If people see it for virtually free, then what reason do they have to pay upwards of $500 for a ticket? Obviously fans will, but will the GP? This is Broadway's biggest crossover to mainstream since Rent i'd say and if they lose some of the GP, then that means they can't charge as much. Or perhaps this will have the inverse and only create more demand now that the 55 Million and counting on Disney+ will have access to it.
Also, as stated in the Hamilton thread, Disney got more than just the rights to this live version for $75M. The got exclusive right to any future Hamilton related content, including a potential Hamilton movie. They also have the distribution rights for the live music from this current film and music from any potential movie in the future. I think in the long run Disney more than makes their money back on the $75M.
A horror movie like that is normally a quick shoot, but if they go into production, they damn well better make sure everyone has a mask on set except for the actors when rolling. Similar to a professional sports or to theater, illnesses running through the cast and crew on movie sets is pretty common.