And what is considered a drug or not is at the discretion of the FDA and other agencies. This is a choice they make not to regulate supplements like drugs. This fact has no bearing on what level of regulation is appropriate for a given chemical. Don't avoid the meaningful discussion by citing trivia.
You're right the FDA decides those categories. But Biogen is the one that created the compound and is pitching it as a drug, when they could've sold it as a nutritional supplement. Why exactly do you think they did that?
Edit: I ask this because my understanding is that the FDA is supposed to make sure drugs are safe and also to oversee drugs of abuse. If a drug is deemed safe and isn't one that's likely to be abused, I don't understand why it's within the FDA's domain to tell a doctor whether they can prescribe it.
But let's assume there is no legal barrier to the doctor prescribing Aduhelm, and somehow you've found a doctor who is going to against the status quo based on inconclusive studies. Which insurers are covering it (certainly not Medicaid or Medicare)? Which pharmacy is stocking it? And where are they getting their supply? Biogen? You think Biogen's lawyers and executives are going to accept high legal exposure (e.g. consumer lawsuits) for an infinitesimally small market?
FDA approval provides a legal and market framework for drugs to be supplied, marketed, and paid for. If your friend who runs Biogen has a spare box of Aduhelm and gifts it to you, it wouldn't be the FDAs problem.
So why can't Aduhelm be treated like an OTC herbal supplement? Well for starters, because Biogen didn't research and develop it with the intention of marketing it as a herbal supplement. So I think the answers to your question are very much related to the answer to "Why doesn't Biogen release Aduhelm as a herbal supplement?"
So OK, let's agree that Aduhelm is now an herbal supplement. The FDA no longer has the authority to ban it from Walgreens. What's your point? The FDA's decision is about Aduhelm's proven effectiveness as a drug, and it has no bearing on whether Biogen wants to sell it as OTC herbal supplement. Do you believe the FDA is what's preventing Biogen from doing that right now?