I was involved in a discussion where somebody had asked if others had thoughts of doing risky things during their manic episodes. Two people commented, including myself. I worried that only relying on a specific set of guidelines established by the diagnostic and Statistical Manual on Mental Disorders fifth edition could lead to disastrous consequences.
Let's say somebody came into a psychiatrist's office. The person has previously read the DSMV and understands the criteria. That person played their cards right to convince the psychiatrist to diagnose them with Bipolar Disorder, when in truth that person might not likely have it at all. Instead, their true motive would have been to get free benzos so they could space out and get high.
On the other end of the spectrum, some people have been misdiagnosed, leading to unwanted and unnecessary medications.
For both of these situations, why can't blood tests and other physical and objective means be used to insure that neither party is in doubt? You can't lie on a blood test or magneto encephalogram, so why not this?
Science is hard, brains are complicated, and the premises of your question that there is not work being done or advancements in this area is false.
There is no known specific cause of bipolar disorder (as for many other psychological disorders). There is no simple statement like "bipolar disorder happens when you are low on XYZ so let's test for XYZ." Bipolar disorder and many others are in fact defined by the DSM based on symptoms - diagnosing them in another way is not the gold standard.
However, all of the suggested biomarkers are some combination of A) Not specific (i.e., are positive for other conditions), B) Not sensitive (i.e., are negative for people that do have bipolar disorder), C) Expensive or invasive (i.e., not really worth doing if they have issues with A and B), or highly dependent on other individual factors.
Because it's not as easy at it may seem.
There is no direct biological distinguishment of any kind in such a case.
It's like some prefer red, some prefer blue, some like both equally.
In order to link this condition to any bio-chemical causes, very long term studies would be needed and the persons with Bipolar Disorder will likely not volunteer for such studies.
It is not excluded that a very long term study may find a bio-chemical distinguishment unique to these individuals but that did not happened yet.
Related references (There are probably hundreds of references. Here's a few):
Semeniken, K. R., & Dudás, B. (2012). Bipolar Disorder: Diagnosis, Neuroanatomical and Biochemical Background. In Clinical, Research and Treatment Approaches to Affective Disorders. InTech. Retrievable from: https://www.intechopen.com/download/pdf/30151
Manji, H. K., Quiroz, J. A., Payne, J. L., Singh, J., Lopes, B. P., Viegas, J. S., & Zarate, C. A. (2003). The underlying neurobiology of bipolar disorder. World Psychiatry, 2(3), 136. PMCID: PMC1525098 PMID: 16946919
I could be wrong, since I'm not a doctor and all, but it's my understanding based on about ten years of studying issues like bipolar disorder online that to be diagnosed with bipolar disorder, as well as other disorders, like OCD, people merely need to have a set of symptoms, which disrupt their lives sufficiently, which hopefully respond to certain kinds of treatment (and of course, they probably need to be diagnosed in order for them to officially have it). This, as opposed to a specific physiological and/or genetic condition that causes or might cause the symptoms. It's not like strep throat where you can test for bacteria for a definitive diagnosis. There could be infinite causes of bipolar disorder as I understand it.
Thus, any tests that could diagnose it might miss a plethora of cases, and many of the people diagnosed by those tests might manage their condition perfectly already (which means they don't have bipolar disorder).
It's my understanding that the aim of such tests would be to assist doctors in making a good diagnosis rather than to replace the doctor's decision.
Nevertheless, there could be other conditions with symptoms similar to bipolar disorder, which do have a definitive underlying cause: e.g. vitamin B12 deficiency. I guess it's probably up to the doctor to decide if the individual also has bipolar disorder.
Anyway, I'm not saying bipolar disorder is all in one's head. At least some of the symptoms are physiological (such as how patients tend to get more manic if they take anti-depressants). I'm sure a lot of doctors use that criteria to help them diagnose the condition already. While I don't know another condition that would match that issue, it's possible there is one. However, just because symptoms are physiological doesn't mean they always have the same cause, which means they could have different methods of diagnosis.
Now, all that being said, while I still think a definitive test is possible, a new way of testing would perhaps be needed. A blood test isn't going to tell you behaviors or how well a person is managing their symptoms, or if the person is using good coping mechanisms that might cause them to not need a diagnosis. A blood test may tell you things that predispose people to behaviors and symptoms, however.
I wrote this answer before I read Bryan Crause's (I just read it). So, sorry that I repeated some of it.