More nuanced than that. The field was always tilted to Key due to multiple big donors who favored GT ties. Batt favored Chadwell, Fritz, and some other names that were not published. GT simply did not have the money to tell those big donors to pound sand and hire who Batt/Cabrera wanted.
To Key's credit, he was willing to take the job with a salary at the lower end of the P5 spectrum and in return get more money for his staff and NIL commitments.
From what I understand, Batt navigated that situation without fracturing the high level donor base. Batt and Cabrera were looking at the long game...and Key isn't a bad coach at all. This fanbase needed some healing after the way Paul Johnson was handled towards the end, and how Collins and Stansbury treated some CPJ supporters.
I think we need to look further than what's going on the first 3 games of the season. The current administration is looking at the bigger picture, and not just making a temporary splash.