I think you're missing the point. someone diagnosing everyone as bipolar (without thought) isn't a good thing. Which was the example given. And 'medcheck' is a pretty derogatory term if you think about it. Psychiatry has allowed it to be reduced to the practice of the 'medcheck' and psychiatrists relegated to drug-pushers. I'm pretty sure this is only the case in the US. you would never describe any other doctor as doing 'med checks'.
To take your example, there is nothing wrong with someone specializing in bipolar disorder. But what separates psychiatrists (good ones at least) from other mental health specialists is the ability to formulate a case from multiple perspectives - biomedical, psychodynamic, cognitive, behavioral, systemic, sociocultural and use this to guide treatment and inform care. Psychiatric care should be about the continuous and ongoing assessment and formulation of the patient, about harnessing the therapeutic relationship, and utilize this to guide treatment, which could be primarily focused on pharmacological management, but is not a 'med check'.
For example a great psychiatrist who specialized in bipolar disorder, like a surgeon must first know when NOT to operate, should NOT be diagnosing everyone as bipolar, but have a firm grasp of the medical and neurological differential for mood disturbances and when to investigate further, as well as the psychiatric differential (which includes depression, substance induced syndromes, BPD, histrionic personality disorder, schizophrenia, pathological gambling, narcissistic personality disorder, and PTSD), but also be able to think about the patient from other perspectives e.g. do the oscillations in elation and depression really represent a deep ambivalence about sexuality and need to alterately express and repress libidinal drive? was elation a paradoxical grief reaction?, does the patient have a sense of hyperpositive self and hyperreactivity to negative emotional stimuli even when experiencing elevated mood?, is there a history of sexual trauma or neglect? how has the patient's sense of self been impacted by a parent with a severe mood disorder?, what cultural explanatory framework does the patient have?
whilst the psychiatrist may primarily focus on pharmacological intervention, and have expertise in 3rd, 4th and 5th line treatments and combinations, they will also have be familiar with substance abuse, borderline personality disorder and anxiety states which are highly comorbid in this population as well as assessment and management of suicide risk. they will be able to engage the patient (and possibly family) collaboratively in care, including discussion of risks and benefits of medication, prenatal counseling, discussion of heritable nature of bipolar. Further they may be able to use various therapeutic skills - such as enhancing motivation to take medication, exploring the meaning of treatment-resistance and emergence of multiple side-effects, education about sleep hygiene, development of relapse signature and coping strategies, working on distress tolerance, as well as being mindful to the social space in which the patient lives - there is no medication that prevents relapse when you experience severe life events, when your social support is no longer there, when you live in a family of high expressed emotion, and these need to be understood and recognized by the great psychiatrist.
Yeah anyone can be good and dishing out xanax and seroquel and bipolar diagnoses. But they are not great or even good psychiatrists. sadly, they are all too common, and great psychiatrists are in the minority.