Why should the FDA have anything to say about it? Hearing aids are neither food nor drugs. Another example of a government agency overstepping its bounds.
As MillCreek said, medical devices. This has come up before. Hearing aid manufacturers claim diagnosing and treating hearing loss is too complex for consumers using consumer devices, specially without the aid of a professional. Plus federal and state law say must be provided by an audiologist, a licensed dispenser or a doctor. Combined with FDA approval process and liability costs, they run $2k to $5k. Ten or twenty years ago, probably justified because fitting DSPs into that tiny of a package was expensive.
Now, your average $40 Bluetooth headset has better technology. It just lacks the certs or calibration. IMHO, and MillCreek could chime in, but it'd be unwise for the manufacturer to have a calibration app specifically claiming for hearing loss. A 'normal' calibration app might be fine. Aftermarket apps might be able to skirt the law or law suits.
Under the law, you can use your $40-$100 Bluetooth headset as a hearing aid. The manufacturer cannot be marketed for a medical condition (ie hearing loss) without the device being certified as a medical device. The other issue is audio amplification across the spectrum can be bad for hearing loss. A hearing aid is supposed to only amplify the frequencies to the point matching the amount of hearing loss. Another reason for their cost. As end users can testify, a lot or most hearing aids are not so calibrated. They also have crap ambient noise filtering.
It is entirely possible to build a consumer device and a smartphone app to calibrate it to probably within 95% accuracy of a professional audiologist. In practice, probably better than a lot of professional audiologists. For probably one tenth the cost of a hearing aid.