I’m surprised at your comment and its willingness to consider cryptocurrency, but I’m not sure that I understand how one might come to the conclusion that the mining portion of it needs to be eliminated. Granted, I am aware of the environmental concerns… but any solution that addresses those concerns will still look alot like mining, only it will have become energy efficient enough that this is no longer a problem.

Even in the future when all bitcoins have been mined, the idea is that miners continue to calculate hashes for the blocks, and that they are compensated for that via transaction fees. If somehow that weren’t required (for whatever reason), presumably government involvement would also wish to control the supply of (virtual) currency much like it does today to attempt to control inflation. The mechanism that they’d use for that would look much like mining (just that only they’d be allowed to do it).

Add on to that “traditional bank involvement”, and we’ve basically reinvented the system that we have now… one where there is no privacy, from the government or private corporations, one where they get to meddle in the supply of currency, where that currency is virtual/digital.