As someone that wasn't old enough at the time but just looking at everything through hindsight, Jay desperately needed an album like BP3 and that's why it sounds like that.
Kingdom Come was a failed comeback because it was rushed and didn't have a strong vision. American Gangster was received well, but it seems like an album that was just there. When Jay was on top, he was the one everybody was talking about. He had to restore that feeling.
With BP3, he was trying to do it all. He had mega pop hits, he mixed it up with the new generation, he was positioning himself as having the hot sound while also calling out artists for trying to be trendy. At times, it sounds confused. The first three tracks sound like old-school Jay and then you have songs like "Reminder" and "Young Forever." I get the feeling that Jay didn't want to be that old man that was left behind in the rap game and BP3 made sure that didn't happen. He was still cool, and he was an even bigger name than he was before he retired.
I saw a video weeks ago where they had Jay perform a version of the NFL on CBS theme song during the intro to Super Bowl XLIV. If BP3 didn't make him hot again, I don't know if he even gets that job.