Denver Center Controller reported an ongoing problem with Denver TRACON not approving direct routing for MEDEVAC aircraft; to help expedite the aircraft.

Narrative

I was training a D-side trainee at the time. Aircraft X filed ZZZ..APA. 20 minutes prior to entering the airspace of Denver Approach; my trainee APREQed the Medevac direct APA (entering their airspace near the arrival fix TBARR) for Medevac status and to avoid weather over LOA routing. We were told 'unable for now' and that they'd call us back. A few minutes later; someone called back and said that the request is denied. We were told to put them over LOA routing. His words were quick and mumbled; so I asked him to repeat that he wanted us to put the Medevac over longer routing. He said that he wanted the aircraft over LOA routing and then he said something about us 'signing' the LOA document that requires this routing for aircraft. I said that this is why we are calling for an APREQ. That person had already hung up the line by this point. He never gave his initials.There were NO other aircraft inbound over the northwest arrival gate and no competing aircraft over the LOA routing. The closest DEN arrival was going to be approximately 8 minutes away from TBARR when Aircraft X entered their airspace; with no other Denver terminal aircraft arriving from the northwest. There were moderately low ceilings in the area along with rain; so I imagine that the skydive aircraft at LMO weren't even going up (if that's a worry for them).This is a systemic issue. Denials on direct routing for Medevac aircraft are occurring multiple times a day. Not allowing priority for Medevac aircraft is against the 7110.65. It is also contrary to the compassion of most humans. We (not me personally) have spoken with several pilots and they are filing Medevac status for flights only when they need it.The controllers at Denver Center have been informed that the management at Denver Approach have told their controllers to not accept any direct routing on Medevac flights. We have actually had a controller state over the recorded line that he would 'get in trouble' for approving direct. It is unacceptable for an air traffic facility to have a vendetta against another facility and; subsequently; put people's lives in danger. And it is even more outrageous that people in the role of management are forcing the workforce to potentially endanger people.I could go on and on about how wrong and upsetting these incidents are for us. I can imagine that many reports are being submitted. Something needs to be done.