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.
So one of the prominent solutions is to hand out financial penalties to the only person who happens to be the sole bread earner in the house, that sound like an excellent idea to me.