My insurance told me that:
As the [drug name] is available over the counter, it is not covered by your health insurance. This would be an out of pocket expense for you.
Do health insurances never cover over-the-counter drugs in the United States?
Health insurances are/were in fact required under the Affordable Care Act to cover certain categories of over-the-counter medications, including:
(See this CMS FAQ article).
Further, many insurance plans cover other OTC drugs, including various forms of prenatal and childhood supplements/vitamins (Folate and Iron supplements in particular), and most/all . See this Pharmacy Times article for additional details.
Third, many insurance plans cover some popular heartburn medications which are available over-the-counter; mentioned for example in this US News article.
In all of these cases, a prescription is still required for coverage; often, you may fill that prescription with over-the-counter medicine at the pharmacy, but you'll have to check out in the pharmacy (if in a general purpose store/supermarket).
"Never" is a strong word, but I've not heard of a health insurance plan covering over-the-counter drugs. Typically, they only cover medicines that are prescribed.
In addition, drugs can only be deductible as medical expenses (or considered qualified medical expenses for payment from a health spending plan such as an HSA or FSA) if they are prescribed by a doctor. The only exception to this is insulin, which is deductible even without a prescription. (See IRS Publication 502 for details.)
In general, insurance cover medications and procedures prescribed by a physician. There are limitations and exceptions, but that is the general rule.
Occasionally, even in an outpatient setting, a doctor will write a prescription for an over-the-counter med, often exactly so insurance will cover it, but most OTCs are less than your Rx deductible anyway.
In the hospital, of course, all medications are by doctor's orders and so are covered.
I can't speak to the entire health insurance industry but over several decades of buying my own insurance, I have been with more than 6 insurance companies (finite sample) and not one paid for medications in OTC strength.
For example, Ibuprofen comes in 200 mg tablets OTC. Prescription doses are available in 400, 600, and 800 mg tablets so if your physician prescribes the larger dose, it's covered. Buy it OTC and it's out of pocket. Ironically, buying it OTC is often much cheaper than the prescription fee, especially when a deductible has not been met.
I'd hold open the possibility that if your employer provided a gold standard plan (not likely these days), OTC might be covered. I haven't seen it.
FWIW, if you're using a non timed release medication in tablet form and the cost of the Rx is much less than the OTC equivalent (perhaps a co-pay after meeting the deductible), ask your MD to prescribe the higher dose and cut the pill in half, assuming the lower dose is what you need. There are many medications where double the strength might only cost 25% more.