... The medical test is asking people how they feel. Depression has a biological basis, but there is no clinical test to tell objectively if someone has depression or not.
I like your comparison. Yes depression is like transgenderism. It is real and it is considered a mental illness, just like transgenderism is a mental illness. To treat depression, do you make the word around the depressed person all gloomy so it matches their mental outlook? Of course not! You try to treat their depression. Same with transgenderism. You shouldn't try to cut up and drug their body to make it look more like the gender they imagine, you try to cure the transgenderism itself and make them content with the body they've got. My message to trans people is, you are perfect just the way you are! Your body is the way its supposed to be! You just need to change how you view it. That is the true, inspiring message trans people need to hear.
The ideal comparison - the mental illness at the root of it all - is gender dysphoria, and psychologists have a pretty good way of treating it. They weren't happy about it yeah, and spent ages trying to find alternative workarounds (even, hilariously, hormone injections for the born gender, which went about as well as you'd think!).
I think your comment betrays a misunderstanding of how psychiatry works. These people are not magicians who can change the composition of your brain with a wave of the wand. A lot of what therapists teach their patients is essentially coping mechanisms that can route certian tendencies into less self-destructive pathways. Gender dysphoria is undoubtedly a condition that untreated self-destructive behaviour: anxiety, isolation, self-harm etc. Any psychiatrist with a patient like that wants primarily to guide them towards less destructive ends.
And here we can easily distinguish from similar phenomena like Body dysmorphic disorder and anorexia nervosa. In those diseases the goal is normally open-ended. A person with anorexia will never be thin enogh; a person with BDD who spends hours fixing their appearance will not be satiated; people who become addicted to plastic surgery never think they are beautiful. In those cases, a shrink will be wrong to recommend their patients chase these self-destructive pathways.
By contrast gender transition is not an inherently self-destructive pathway, but a fairly well-studied process with a discrete end and - most importantly - alleviates symptoms of GD. For a shrink this is success. They don't want you to deny the reality of your own thoughts in, in other words. Your suggestion would be the equivalent of saying "Be more happy! Stop thinking bad thoughts!" to every depressive.