i dont think there is anyway that banks could be sued or blamed for using a bitcoin type block chain, but even if that does cause bitcoin to die down, other coins will just take the lead with innovations
I would think that you could sue banks if they copy your idea (in this case, blockchain). But really, "invest in blockchain", the banks aren't going to do this. Bitcoin will not die down because of this. If this does happen, some altcoin will just take over.
I think it's inevitable that the banks will use their own private blockchains but it wont kill bitcoin. Bitcoin is meant to exist outside of the banks and central authorities so it will continue to operate independently as we will always need a decentralized currency to avoid censorship and manipulation by central banks. Bitcoin's potential is far greater than whether banks use it.
Bitcoin was made to be a currency that you can use instead of fiat. Banks will try kill Bitcoin, but they won't succeed.