I think you are missing some important things here. Pakistan players are not allowed to play in IPL because of the political situation between both the two countries. As far as i know , the pakistan board will also not allow players to play in IPL.
And why would BBL ban West Indies ? They will never ban them as every league wants good international players to come and play the league. If leagues start banning international players, no one will be willing to watch tournaments with national players only.
With too much politics involved in cricket specially between Pakistan and India most chances we will have no solid and good policy in ICC for many things and with this all BCCI will take some good advantage as currently they are very strong and having upper hand with the help of money involved in cricket. As many times few Indian and Pakistan members already post that there is no solution between these two countries problems in next one decade so forget about any positive link and BCCI is taking full advantage of their relationship with ECB, CA and CSA because now they are ignoring many other countries as well which are not profitable for their marketing purpose.
Agree with this statement, BBL never ban any player or country as they need some good foreign players for their league, and it's helping them for having quality game in their league.
It could have been a better experience if both IPL and PSL allowed both countries players but to be realistic, both countries do not need other country's players or support to make them successful. IPL is a successful league without any Pakistani players and similarly, PSL is a great league without the Indian players.