I wonder what high credit card fees you are talking about. As a consumer, I pay none of them. In fact, I get money back every time I purchase something with my credit card (in addition to getting a bunch of other benefits, like purchase protection, extended insurance/warranty, ability to charge back, etc).
As far as I know, none of this is available in the cryptocurrency world, and more importantly, all of the cryptocurrencies that I know of do charge a transaction fee, which cannot compete with $0 flat (not to mention cash back).
Crypto currencies have interesting features, but low transaction fees vs CC isn't one of them.