Banks and the CC companies do a lot of things, but let's talk about lending.
People want loans. They want them so much, they're willing to pay for the money they get, in the form of interest. This is true now, it's likely to be true in the future. Bitcoin won't change that.
You seem to be seeing the world out of the eyes of the average anglosaxon...
Having lived in Switzerland for a few years I can tell you that there are considerable groups of people who do not live on debt -- I know of only one person who has a loan there -- specifically a mortgage (house-ownership in Switzerland is uncommon -- most people rent, which means that mortgages are rare -- credit cards do exist but are mostly paid off monthly), most of the Swiss do not rely on the bank for a loan, instead they rely on the bank to keep their money safe, and less often to manage their investments.
There are certainly loans given out for businesses -- this is something I currently know too little about to compare.
Whether or not the above is a factor in the higher quality of life in Switzerland is certainly debatable.