I don't at all care about the pot, or really even the immaturity.
I just don't think he is a terribly good ball player. I am looking at his career stats, and he has never been above league average in any statistical category, and has in fact been far below it at points. His eFG% and TS% are both abysmal, as is his points per play. He is a very inefficient player, which does not fit our system well.
That said, it is possible for him to improve. People make the comparison with Odom. Certainly, Odom was trash as a Clipper, and improved remarkably in subsequent years. However, it is worth noting that even when Odom was a Clipper, his TS%/eFG%/points per shot were all ABOVE the league average. His passing, too, was remarkable (he averaged 8.2 assists per 48 minutes, where the league average for his position is 2.6). His defense was pretty good too, getting above average block and steal numbers. The reason he wasn't very good is because he was a terrible rebounder and help defender, and he turned the ball over a lot.
So, it IS possible for Beasley to improve. However, Odom I do not think is a good comparison, because Odom was already a very efficient player, and his weaknesses were in areas that are much easier to improve on (boxing out, rotations, limiting turnovers) than Beasley.