The "sequential treatment" or "tailored treatment" approach is at least plausible and what is done in practice, yes, if the prescribing doctor is good, and if this is feasible for the patient.

However, since this takes time, and most depression is temporary, it is hard to know if you really are tailoring the medication to the person in many cases, or it has just been long enough you are seeing regression to the mean (or a placebo response, which is still strong even in treatment-resistant depression https://jamanetwork.com/journals/jamanetworkopen/fullarticle...).

There aren't really any double-blinded or even just properly placebo-controlled / no-treatment controlled studies to test this, but the closest thing to looking at the sequential approach also doesn't find very impressive results (https://bmjopen.bmj.com/content/13/7/e063095.abstract).

I do believe the drugs help some people, and almost certainly take some experimentation / tailoring. The average effects are just very weak.