There were many things Hazell did wrong as a head coach. he was clearly in over his head. No coach should ever be compared to Hazell. Period !!!!!
In evaluating Brohm, I suggest you compare him to his contemporaries at similar schools and salary. Is he earning the money he is being paid? I am a firm believer that Purdue should be better than any non-power 5 school. I'm a firm believer that Purdue should be as good as IU, U of I, NW, Rutgers, Maryland, Cincy, Minn, Vandy, Iowa, Cal, Duke, Southern Miss, USF, Boston College, USAF, Army, Navy, USF, Miss , Miss St, GT, TCU, Baylor, K st, ISU, UK, Col, Col St, Boise st and many others. I don't believe Purdue will ever be a consistent Top 10 team. but I do expect them to be a top 25-40 team.
I also don't believe in giving a coach 4-5 years before evaluating his progress. in this day of transfer portals, a smart coach can rebuild fast. NW picked up a 5 star transfer QB. Illinois picked up a 5 star transfer TE. IU picked up a guy from Utah(?). Brohm brought in his share of grad transfers for a quick fix. In evaluating a coach, there are trends and activities both on and off the field that will indicate if a coach will be successful. And you can see those trends developing in the first 2-3 months. I could see those trends in Hazell before he ever coached a game.
Lastly, sometimes a school wants more success than a coach can provide. there are some schools where going 8-4 every year is just not good enough. Look at Nebraska, Michigan, Auburn, LSU, USC, ND, etc.. they expect more for their money. While you may love Brohm if he went 8-4 at Purdue, he'd be fired at many schools if that was the best he could do.
that's why I say, never compare a coach or a team to their previous coach. Compare them against their contemporaries at similar schools and similar salaries. the Minnesota game should be a very good evaluation game. the schools are similar. the talent is about equal. and both coaches arrived at the same time to develop their programs. It will be a good test and also measurement tool.