It's not a bad idea to get training and do them on some regular basis, if only take what you can get by doing an abbreviated version. Remember SCID is very long (1.5 hours), and even MINI is relatively long (let's say give it 30-45 min to be generous), and the purpose of a clinical intake interview is more than simply diagnostic accuracy (i.e. you need to assess for other "big picture" items, like family support, medication tolerability, other medical comorbidities, fit for various psychotherapy modalities, etc), and in many cases might have to do other additional housekeeping things like urine tox screen, physical exam, payment and paperwork, etc. etc.
I had a discussion with someone recently about this: why not just have a masters level clinician do a SCID and give you a list of diagnosis, and just write meds based on some algorithm. IMO this is not more efficient 1) the label, say of MDD, doesn't dictate my med use, has to do with things outside of diagnoses, which means I'd have to repeat a bunch of random questions anyway. 2) in general, most psychiatrists are seeing things that are more complex than a garden variety MDD diagnosis, like a list of random meds, failed trials, suicidality, psychosis, co-morbidities, etc. Diagnostic labels don't address issues relating to the severity and clinical judgement calls relating to the "design" of the right regimen if this makes sense.
Missed diagnoses in psychiatry is *extremely common*, depending on the context. In fact, sometimes what is "missed" is simply intentionally ignored for various reasons (i.e. reimbursement and other systems related issues). A good thorough outpatient intake can be easily 90min+, and for child can be 3 hours+, but most public facilities do not allow for this. A different way to say this is that you can conceptualize your role in this as an extended evaluation, and screen for issues as appropriate.