That's an interesting question you pose, in fact, I never thought of that. It indeed makes sense, for many of us depression can be a real possibility and reality and diapers or a combination of diapers and baby-time can be seen as the ultimate form of stress relief and therapy. Doctors can recommend forms of therapy, they can also prescribe pills, but the downside to the latter is that pills/anti-depressants can form a dependency in the individual and certain types of can be quite harmful. So, diapers really are a much more healthy alternative to pills and drugs, especially pills and drugs that are addictive and may exacerbate your depressive symptoms.
I think the real question is though, would a doctor ever provide a prescription for diapers over pills?
While I definitely think diapers and baby-time are a healthy alternative form of stress relief, I don't think a doctor could or would ever provide them as a prescription. For one thing, ABDL is quite rare, if the doctor had an ABDL patient and was understanding, maybe he would provide a prescription, but even that seems doubtful. I've only ever heard of diapers being prescribed to people with moderate to severe incontinence, even those with light incontinence are given alternative forms of regulating it, going further, if you read the medical websites for most over the counter Adult briefs they suggest adult briefs/diapers as a last resort.
Furthermore, the medical system in the states gives doctors more incentive for referring people and prescribing drugs than for prescribing alternative methods that might actually work. It is more financially lucrative for a medical professional this way even if this behaviour is detrimental to the patient.
Also, prescribing diapers for stress relief and depression relief could never really catch on, it's only a viable form of relief for those who are interested in diapers and ABDL. In order for doctor's to even consider prescribing them, diapers would have to be a known form of stress and depression relief for everyone and anyone who has suffered depression, regular everyday people, not just people within our relatively small community. Think about it for a moment, you are a regular joe and you have severe depression and then your doctor prescribes you diapers to relieve it, the immediate reaction would be WTF, followed by this person likely seeking out another professional.
Finally, what type of precedent would it set? Whether diapers were an applicable prescription for ABDL's and regular folks would it just end with diapers? For instance, you could make the argument that other aspects of ABDL curbs stress, depression and anxiety, playing with stuffies, drinking from bottles, shaking rattles and cuddling a caregiver help me relieve stress as an ABDL, would those behaviours and acts be prescribed as well? Would a doctor refer you to a caregiver and prescribe you an Adult Bottle or an Adult Pacifier in addition to your diapers? I certainly don't think so.
So, once again an intriguing question. In a perfect world where ABDL was a more accepted behaviour, I think the idea of ABDL's being prescribed diapers for their emotional, physical and psychological benefit would be a great thing and quite possibly a standardized practice. In the real world, however, such a thing will never truly be because of the stigma surrounding diapers, the fact that not every patient will have ABDL tendencies and thus, will not be interested in wearing diapers even as a form of stress relief. I agree with you, diapers would be an excellent alternative to depression, anxiety and stress relief, but it is ultimately wishful thinking to believe that a doctor would prescribe them, after all, there are too many practical, commonsensical truths/facts that would prevent it.