While it is actually possible that the banks would, in the future, ban cryptocurrencies transactions, there's no way the banks can ban P2P transactions.
P2P is what early adopter of bitcoin and other cryptocurrencies use before exchanges that allow direct deposit of fiat currencies come into play. The only disadvantage is that it requires that you find a reliable person to exchange with.
There's no way for them to ban P2P transactions unless they ask help from the authorities to track and stop those people who are being involved and pushing P2P transactions.
It's very usual for some business to track their competitors and lose them through asking help from the authorities.