Stumbling in a hangover to appointments on "work days" and giving everyone the same diagnosis as the last (and likely whatever sickness they themselves had recently). Also giving everyone fluids and an ativan so the patient says - "i feel much better doc".
It's kind of an open secret that the ER just gives a diagnosis of dehydration, provides fluids and ativan to get the pipe rolling and charge $4k a pop. Sure they might catch a case of undiagnosed covid, rsv or something else from time to time.
Also I'm not kidding but I would LOVE such a show.
Chicago MD has some of the aspects you mention, especially overloaded, drug abuse, blame, police interactions.
New Amsterdam attacks it by the main character trying to solve the problems and running into bureaucracy.
People really don't understand the dire and primitive state of current medicine.
We are in the dark ages. We don't know why most drugs work; we have some notional idea but it's often an after-the-fact fiction that we tell. We don't know what causes the majority of diseases. In many cases we don't have treatments for the underlying problems, we only have treatments for symptoms.
If you want to see House MD, then tell your congresspeople and senators to invest in funding medical research so we can one day maybe leave the dark ages.