What's the functional difference between that and a clinical trial, from the perspective of the patients?

It would be essentially a clinical trial, an open-label one.

There even have been several blinded trials, that were discontinued mid-way, because the drugs being tested were so effective.

To continue giving placebo and denying obvious cure would be unethical, and so the trial was stopped, placebo arm cancelled - and everyone got the actual medicine.

in a trial, you get invited and you might be placeboed out as a control.

in the “just try it and see scenario”, you offer it as a possibility, and everyone who ops in, gets it.

it might not be as scientifically rigorous, but that's a big difference to the patient who suffers from receiving a placebo instead of the real deal