BCCI might be bad in PR or not, that's another discussion because when it comes to court cases in regard to any compensation claim. BCCI is ruthless as there you need facts, not PR and they focus on the latter.
BCCI only issue is with visiting Pakistan if this angle creates problems for ACC then I won't mind if all ACC members get together and kick out BCCI.
Kicking out BCCI is not the solution, because India contributes to almost the entire revenue for ACC during Asia Cup and other competitions. Imposing financial penalties maybe an option. But even here, there is no guarantee that the BCCI will follow the majority decision. I don't know how much Jay Shah care about the position as ACC president. His ultimate target maybe the chairman post of ICC. In order to reach there, he needs to have warm relationship with all the ACC/ICC members, including Pakistan.
Most chances anything like this is not possible because ACC is currently controlled by BCCI like they are controlling ICC, and they have good support from countries like Afghanistan and Bangladesh which never been going into favor of Pakistan just because of personal issues, but the worst thing is we never have any positive solution for this these both are going to bite each other and can't live happily as we have at the end of Hindi movies.
But one thing is sure ACC will be never ideal sports organization as they are having two big which are the worst enemies for last 75 years and never want to sit on table for positive talk as we have ideal situation in Africa and CONMEBOL which are also developing like subcontinent but still doing amazing job for the sports.