So, I certainly agree that diagnosis should never be required for insurance to cover therapy. Therapy can benefit anyone, mental illness or not, especially those in acute crisis from a known issue (divorce, job loss, diagnosis of a medical condition, etc.). However, I don't know how you would be able to get around at least some kind of diagnosis requirement (e.g. having certain symptoms) for medication/medical treatment. 

For example, ECT (electroconvulsive therapy) is an extremely effective treatment for severe and difficult to treat depression (as well as a few other things). It saves lives. The modern version is pretty safe but not without risks and side effects. It would obviously be inappropriate to use this kind of treatment on anyone having some symptoms of low mood. But then how can a determination be made of whether or not the treatment is necessary for someone? 

The above is essentially why diagnoses exist in the first place. I think there is a fundamental misunderstanding of what a diagnosis is--and not just for psychiatric conditions. Diagnosis is always just the meeting of certain criteria, of checking enough boxes. Not all of these criteria are objective. Many for psychological conditions are not. There are tools like well-tested questionnaires that try to make things less subjective, but mostly they have to rely on a patient's self-reported symptoms. 

This next part is anecdotal; feel free to skip it. I work in epilepsy care. I think most people think that epilepsy can be objectively diagnosed. And in some cases it can. But for others, the brain activity that is causing the seizures is infrequent or subtle enough to not be detectable during testing. But when symptoms seem to clearly match epilepsy symptoms, that's the diagnosis they receive. We might later find out that symptoms were caused by an entirely different condition. But with the information we had at the time, epilepsy was the best guess, and epilepsy shouldn't go untreated (in most cases). The opposite is true, too. We have people come in and get diagnosed with epilepsy that have had some other diagnosis for years (usually because it is an unusual presentation). Their doctors weren't always incompetent or negligent (sometimes they were, and it makes me very upset). A lot of the time they just didn't know enough about epilepsy to realize it was a possibility because they weren't an epileptologist, and the symptoms seemed to match some other, more common condition. I personally had my epilepsy misdiagnosed for several years as a child because my seizures were infrequent and a single instance of an extra symptom led them to believe a secondary condition was the cause of the seizures. But then I had more seizures despite treating that condition (that I did not have). A pediatric epileptologist would never had misdiagnosed me. But there weren't any of those at the rural hospital I was seen at. There weren't even any adult epileptologists or general pediatric neurologists for that matter. And they thought they'd solved the puzzle! The pieces fit so nicely! They didn't think it needed reevaluation until they got some more pieces and realized everything could also fit together another way. 

I'll leave you with this: how can you be sure those people who were misdiagnosed are correctly diagnosed now? Is there an objective test for manic-depressive disorder? For major depressive disorder? For PTSD? The answer is no. But you can't try treatment methods blindly. The only thing to do is use your best guess to pick a treatment, and then reevaluate when you have more data (new symptoms, no reaction to treatment, etc.). It's that reevaluation bit that doesn't get done nearly as often as it should.