Straight answer: for supplements and everyday prescriptions like blood pressure or cholesterol medication, no.
For controlled substances — ADHD medication, painkillers, sleep medication, anxiety medication — it's a real thing and we're not going to pretend otherwise. Most states have some version of a law requiring prescriptions to stay in the labeled container, and if you're stopped by police with unlabeled pills and can't show they're yours, some states treat that as unlawful possession.
Penalties range from a fine to a misdemeanor.In practice, courts allow reasonable repackaging, and having proof of your prescription resolves it. So: Take a photo of your pharmacy labels and keep it on your phone. That's ten seconds and it covers you almost everywhere.
If you take a controlled substance, keep that one in its labeled bottle and use the pouches for everything else. This isn't legal advice and the rules differ by state — check yours if you're unsure.