This is, in fact, pretty much the exact procedure: try one type of treatment or medication, see if it's obviously helping, and if it isn't try a different treatment or medication. It's imprecise but it's the best we have.
The problem is that taking certain psychotropic medications changes your brain chemistry. It’s not as simple as it sounds. It’s not like trying on shoes. The brain is dynamic and drugs alter it, as does life experience, talk therapy, disease, aging, etc…
That’s a statement of fact, but not intrinsically a problem. Being alive changes your brain chemistry.