The only reason why BCCI is desperate for a single match per year against Pakistan is simply because one match is the biggest revenue generator for BCCI. One match between Pakistan and India earns more revenue compared to an IPL season.
This Is why BCCI along with GoI, and yes there is a connection given Jay Shah, will cowardly deny visas for Pakistan fans, but will never, EVER, have the courage to deny the Pakistan team from playing in India, or refuse point blank to play Pakistan elsewhere.
Think about it, if India doesn't want to play Pakistan, then why doesn't the BCCI simply refuse outright to play Pakistan across all comps? Boycott Pakistan should be their motto!
To top it off, you got Indians claiming the rivalry is dead. Nope, it is alive, and it is the ultimate cash cow for the BCCI for an eternity, more than the IPL, more than an ICC comp, more than any bilateral.
This is why BCCI begged the ICC to ensure there is always a Pakistan vs India clash in any white ball ICC tournament.