Doctors "can" do lots of things. "Will they" and "should they" is another question. There are truely thousands of blood tests costing hundreds of dollars each which are now easily available. This does not oblige a doctor to order them if they do not believe that it will change their treatment of a patient. Patients often request obscure, expensive tests because of things they read online (recommendations from chat groups and boards) and go to their doctor requesting hundreds of dollars worth of tests because they read it might help. They only request it and expect it because their insurance pays for it, but there is truely a very high cost to someone for ordering and running these tests. Also the question remains "what if the result is abnormal?" What good would that do? If testosterone is abnormally high that needs to be looked into. If it is low that needs to be looked into. But if DHT is higher than you want all you can do is take finasteride or dutasteride. If it is low on finasteride or dutasteride good, they are working. If it is high on finasteride or dutasteride what else are you going to do? NOTHING. The endocrinologist is probably reluctant to order a test that won't tell him anything useful and will not lead to further evaluation or change in treatment.
Male pattern baldness happens with normal levels of DHT. Having DHT and male pattern baldness is normal... so, ?What good is a blood test for you? You know you can reduce DHT 70% by taking finasteride. If you have male pattern baldness you should take finasteride regardless of your DHT level. ?What else can you do?
If you think it would change your treatment talk to him and try to convince him you need it by showing him how it would change what you are doing if it's abnormal.