Melatonin is the hormone that regulates sleep normally. You're taking additional sleep hormone by taking it orally. So sleep is melatonin.
It's the hormone that is theorized to be involved in the "blue light" sleep effect. When the high-wavelength cones are stimulated, melatonin release is reduced, according to current theory. [0]
"You're taking additional sleep hormone by taking it orally. So sleep is melatonin."
Sleep, and sleep with additional sleep hormone aren't the same thing by definition.
> So sleep is melatonin.
By taking melatonin orally you can get levels which aren't possible endogenously. So melatonin supplements != "vanilla" sleep.
Melatonin is also a mitochondrial anti-oxidant, so may benefit people with "brain fog". Such people may well have to take a supplement to get the maximum benefit. A benefit which can't be reached with natural (what is natural?) sleep.
In older individuals, the endogenous production of melatonin is reduced (happens when people get older). They may also benefit for supplementation. A benefit they couldn't get without it! No matter if they wear blue light blocking glasses, or have f.lux on all their machines.
Sometimes people have to do things at night. Where there's light. It's modern life. They can't go back in time and not be exposed to that light. They may also benefit from supplementation.
One could describe it as enhanced sleep.