Well, I mean, that depends on the shape of reform. If you mean what the ACA did, no.

Medicare for All? Maybe.

> As you're cutting out all of the admin overhead, billing here and there, everywhere.

A significant share, as I understand it, of that cross-billing is to get an official denial from a higher-priority payer to show to another payer; my intuition would be that more coverage and security of payments would, even in a move to single payer, increase final number of payments unless actual payments are grouped and consolidated rather than paid individually as approved.