Crypto-currency is not decentralised by nature. Bitcoin, dogecoin etc. are just one model. There are other models for crypto currency that involve issuing banks and have other advantages - offline transactions and no crazy waste-of-electricity hashing races.

One question then, what motive is there to support the blockchain once mining has ended?

For BitCoin, it'll be transaction fees. In order for your transaction to be proceeded (which requires a form of mining), you'll have to pay a small fee.

So in order to process you non-bank transactions you need to use a centralized processor that charges you a fee for transferring your money?