I researched it , the president or former presidents do not run either the DNC or the RNC. The chairpersons are elected by the membership. At least that's the way it's suppose to be. Biden hasn't abused the DNC. trump is doing inappropriate things in regards to the RNC and this needs to be very carefully monitored. You owe that to the voters.Because he's the leader of the party. Biden selected the Chair of the DNC.
To start paying this legal bills, it would take a vote of the membership. There are currently over 160 members.