Why aren't any advancements being made in physically diagnosing Bipolar and other psychiatric disorders?
Short Answer

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.

Longer Answer

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.

That said, you seem to be implying especially in your comment "why isn't one being developed" that this isn't an active area of research. It is - a helpful search term for you will be 'biomarker'; Google Scholar returns 4,480 results since 2017 for ("bipolar disorder" "biomarker").

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.