The effects of antidepressant medications - and their combinations - can vary greatly from individual to individual. Even if they work, their effects may diminish over time.
If you can gain substantial relief from therapy alone, then by all means pursue that. In most cases of severe depression, though, I suspect most doctors would want to prescribe an AD too.
Unfortunately, the insurance side of things may interfere with what you and your doctors want to do.
Keep complaining.
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My dog

mastered the "fetch" command. He would communicate he wanted something, and I would fetch it.