Water is the largest unlisted ingredient in most cocktails. It arrives from melting ice during mixing, and the quantity is deliberate rather than incidental.
Chilling and dilution cannot be separated
Ice cools a drink by absorbing heat as it melts, so the water added is a direct consequence of the cooling achieved.
There is no way to reach serving temperature with ice without also taking on water, which is why the recipe assumes it.
A finished drink mixed properly is commonly around a quarter water by volume, and the undiluted recipe would be undrinkably strong.
Dilution changes what the drink smells like
Aroma compounds partition between the liquid and the air above it, and lowering the alcohol concentration pushes more of them into the air.
This is the same reason a drop of water opens up a neat spirit, and it applies with more force to a mixed drink.
Too little dilution leaves the aroma locked in and the alcohol dominant on the nose.
Temperature and dilution are not the same target
A drink can be cold and under-diluted if it was stirred briefly with very cold ice, and warm and over-diluted if it was stirred with wet ice from a melting bin.
Bartenders judge by feel on the outside of the mixing glass and by the volume in the pour, because neither variable is visible in the liquid itself.
The two only move together when the ice is in a consistent condition, which is why ice handling is treated as a discipline rather than a detail.
Under-dilution and over-dilution fail differently
An under-diluted drink tastes hot, closed and sharp, with the individual ingredients still identifiable rather than integrated.
An over-diluted one tastes watery and flat, with the acidity and sweetness both muted and nothing to hold the drink together.
The window between the two is narrower than most home bartenders expect, and it moves depending on the ice being used.
Ice condition controls the rate
Ice straight from a freezer is well below freezing point and spends its first seconds warming rather than melting.
Ice that has been sitting out is already at the melting point and dilutes immediately, so the same stirring time produces a different result.
Wet ice from a bin with standing water dilutes fastest of all, which is why service bars drain their wells.
Pre-diluted and batched drinks
Batching a drink in advance requires adding the water directly, because the batch will be chilled without ice at service.
The quantity is measured rather than estimated, which is one of the few places dilution becomes an explicit number in a recipe.
Getting it wrong is unrecoverable at that point, since the correction cannot be made once the batch is bottled and sold by the glass.