There is potential that the teams attached to the shows have also weighed in about where they want the show to be featured. A few years ago, Scarlett Johansson got into a legal battle with Disney over a guarantee she had that the Black Widow movie would have a period of exclusivity in theaters but then Disney put it on Disney+ for streaming at the same time.
Having violated their agreement, Johansson successfully sued Disney. The minds behind the shows that HBO has moved from exclusively being on Max might have had similar preferences.
Regardless, with Max now losing exclusivity for so many of the big-name shows it had coming out, it will be curious to see what use HBO sees in Max for the long haul.