Banks,  central banks,  governments,   large corporations probably.  it would be a closed network  so while anyone could mine they would  have  to do so through a  controlled mining pool  and get paid in local currency.  Most world currencies  would be pegged to govcoins  though,  like gold after the Bretton woods agreement. transaction blocks could still be made public,  and the owners of addresses would be on public record.
 
This is not a desirable scenario obviously, but  I'm wondering is  this likely,  or what the better alternatives are. How could the current version of bitcoin be made suitable and desirable for mass use by banks and governments,  or their future replacements.