It has nothing to do with push. Blu had every label at his door after Beneath The Heavens. He was tall, light skinned, handsome (pause), and melodic: that's the blueprint. He did his own thing for a bit (the Mainframe album, Her Favorite Color, etc) before signing with Warner Bros and dropping a Yeezus-esque album with no commercial viability. All during this period he was abusing drugs and slowly fukking up live shows, relationships, etc.
Blu had a shot, he turned it down because he never wanted to be big. And he ruined his career with drugs; dude was too broke to pay engineers to master his projects lol. Let's not forget Kendrick and Q opened up for a Blu show years ago in Cali. TDE lapped Dirty Science and the rest is history.