The solution to this is way easier than blockchain: Just regulate them. Personal credit card fees in the EU are capped at 0.3% and everybody is better off.
I think the necessity for regulation shows that unregulated payment processors leads to market failure (due to the nature of that market under current non-blockchain tech). Regulatuon fixes this market failure, but I see regulation as a last resort due to its being a high overhead solution (you rely on courts to interpret the regulations or check the statutory agencies, on the agencies to do their work, on lawmakers to keep the laws up to date). Of course, it is an open question as to whether blockchain tech can lead to the payment processor market not to suffer from market failure if unregulated.
> The solution to this is way easier than blockchain: Just regulate them.
Regulation is not easier. I & my merchant can use blockchain today, without any permission or buy-in from a regulatory body.
This is an example of automation taking a job. As an engineer and small(er, more efficient, more effective, more fair, more predictable) government enthusiast, it thrills me to see that we're automating away the jobs of bankers and regulators around the world.