Also you’re right as Amir did perform well for Karachi Kings, but he was dropped as he had failed to pick wickets during Pakistan tour of England.
Lastly if he keeps performing well in domestic cricket, then I’m sure that he’ll find his way back in Pakistan’s Cricket team soon.
I can understand if players prefer LPL or other "smaller" leagues instead of BBL. There's no doubt that BBL is one of the most popular franchise T20 leagues out there. But they have some very ridiculous limitations, such as very low salary cap and a limit of just 2 overseas players per team.
BBL has increased the limit of international players from two to three recently which is encouraging for the overseas players and also it will create more interest in the matches.
https://cricketaddictor.com/cricket/bbl-2020-21-three-foreign-players-playing-xi/