Because, technically, the antiphon Hosanna doesn't accompany the procession of the priest and ministers towards the sanctuary, but their approach to the place where the people are gathered where the Procession or the Solemn Entrance is started.
Palm Sunday does have an Introit, however, but it is only sung at Masses at which the Solemn Entrance is not held, and a Simple Entrance takes its place.
Compare with the first proper of the Presentation of the Lord (February 2): this is also called an antiphon and not an Introit.
It might be be difficult to sing that Introit, because it it not in the Gradual or in the 1961 Gradual. It's in the 1908, though ("Ante sex dies solémnis Paschæ").
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