Surely the point of declaring "Minimum Fuel" means exactly that though, that any further delay will put the aircraft into a "Pan-pan" state. Saying "HeavyJet123 Minimum fuel, any further delay and we will have to declare a Pan" just blocks up the RT on what is potentially already a congested frequency and is the reason we have the "Minimum fuel" call to begin with.
Minimum fuel is used to alert ATC that you're getting tight, but not in trouble yet and to focus their minds, and ideally means that they will give you as accurate an EAT as possible ASAP, if you feel you need priority to land, then declare a Pan or Mayday as appropriate.