The problem is that the government loves cracking down on crime through the financial system - terrorism, drugs, IP issues, firearms, etc, etc. It's the one tool they've used again and again...because it works.
So they'll never give financial institution carte blanche immunity, because they rely on them to choke off the money for illegal activities. And even if they did give immunity, you know they'll turn around a say "well, we didn't mean you could just ignore blatantly illegal activity" and the banks will fall into line.
The meta-problem is that both liberal and conservative politicians are on board with with cracking down through the financial system for one reason or another.
If you see comments calling for payment processors to be dumb money pipes free of liability, those are likely coming from libertarians.