This was always about going after Kanye Trump-Lovin ass, not helping promote Pusha T who’s never been a household name.
Kanye sent Pusha at Drake because he ain’t want no smoke.
Pusha is too small for Drake to beef with. Drake mostly goes after rappers with some type of name value (Meek, Ye, Jay, etc...).
Remember how in ‘Dre Day’, Dr. Dre kept his attention on Eazy, while his Lil homie Snoop focused mainly on Tim Dogg. I know some of y’all hate to hear this, but Pusha is equivalent to Tim Dogg in this comparison. The problem is that Drake doesn’t have a Lil homie (Snoop) that he can send at the irrelevant rapper (Tim Dogg/Pusha T), while he focuses completely on the boss (Eazy E/Kanye West).