If you declare minimum fuel you'll be asked for your latest divert time from either the pattern or the field. You'll be then sequenced appropriately with no delay. In 23 years of ATC I've never heard of other aircraft being asked to surrender slots, the ATC that allegedly did this must have been suffering a mental breakdown?
It's medevac & hosp priority now. Whenever aircraft have advised a sick pax on board, I don't give a flying you know what whether you've declared medevac or not. You'll get priority, I tell the flow & I've never, ever had a flow insist on the aircraft declaring a phase before being processed with priority.
Over the years I've had several pans & one mayday. I've had several calls that should have been pans & maydays but those words weren't spoken. Phases were declared by ATC's, their supervisors etc because 'common sense' was used. I've had an A320 return to departure point because of 'control issues'. 'Are ops normal'? 'Affirm' was the answer. Do you think a phase wasn't declared? If ops are normal why are you returning to destination?
A question for the techie's, are you being advised not declare pans? If you are not, why aren't you declaring a pan if it clearly is?