Mood disorders might have underlying causes, but the diagnosis and definition is entirely based on the symptoms. Comparing it to having a cold is a bit misleading. It's more like having a couch, or itchy throat, that may be caused by cold, but it's not the diagnosis you'd get.
Could you cure a cough with couch syrup? Could you cure a sore throat with pain killers?
Antidepressants makes the basis for a depression diagnosis go away for some of those who are treated. Having no measurable level of depression is probably the closest we will ever get to a cure of depression at large.
If the depression is caused by something specific, say a vitamin deficiency, that underlying issue would of course not be treated by SSRI. But we don't know enough to say that there always is something specific causing the symptoms. What if the issue is actually a serotonin deficiency? Just like some people naturally produce to little vitamin D and have to take supplements.
What if not all DNA sequences lead to a happy life? There's nothing in evolution that enforces that all offspring has to be happy for survival to happen.
In the same way that cough syrup will never cure a cold, antidepressants alone will never cure depression.