Like most topics in modern medicine, there is literature on both sides of the issue. Hopefully the body of literature will continue to grow with large scale quality studies to the point where meta-analysis can be performed.
For orthotics, it's a fairly mixed bag in studies, and the results of a functional orthotic device depend a lot on how good the casts and choice of materials is (which is why the mats or foam are pretty suspect). Overall, there is almost certainly more research supporting orthotics than not. Most DPMs I've been in clinic with will start the patient off with an OTC orthotic in hopes of saving them money, and they can then progress to a more expensive custom device if the patient isn't getting good enough results. Some people get satisfactory results from just the OTC inserts, some progress to custom orthotics and get good results there, and others have to keep trying other treatments.
In the end, the proof is in the results; the attendings who have helped hundreds of patients know a lot more than students and residents who have mostly just read a few articles or casted patients but never seen them at follow-up. There are some podiatrists here in Miami who offer a full refund to patients if they are not satisfied with their custom orthotics, and they barely have any returned (usually in patients with feet so flat that surgery or other advanced treatments are really their only viable options). When you see patient after patient willing to spend $400 out of pocket for new orthotics due to the benefit they got from their last pair over the previous few years, I'd say they certainly work for some people
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You certainly don't have to use every treatment you learn in school, but you want to know what's out there and available. Ultimately, like I said, you will use a combo of the literature, accepted standards of care, and, mainly, your clinical judgement/experience to decide what's best each individual case. If you went to 10 different pods for painful flatfoot, they'd all at least mention orthotics as a treatment option.