I don't think they can sell their fan base on Cuonzo Martin (and you could probably say the same about Alford).
He's done a nice job at Missouri State, and he's going to be a very good coach at a big school someday, but I think their fans expect to get more than a coach who has 1 NIT trip and 1 CIT trip in 3 seasons.
The reason I think getting the fans fully on board with the hire is crucial is because they had horrible attendance problems this season. Their attendance, especially in the nonconference, was horrible for a team ranked in the top 15 much of that time. Out of 10 nonconference home games, 7 of them drew under 10,000 people. They can't afford to make a hire that any portion of their fan base views as "blah".
If the Matt Painter rumors have any legs and he does go to Missouri, I could easily see Cuonzo Martin taking over at Purdue.
There are too many reasons why it makes sense for Alford to get this job, especially if he was interested in it after Quin Snyder was fired.