Tatiana asked: "Should not [La moitié de baguette] work as well as [Une demi-baguette]?

Bonjour Tatiana !

Here there's a nuance of meaning between une demi-baguette and la moitié de [la] baguette.

Une demi-baguette means "one half of baguette" or "half a baguette": here it's a general characteristic of the object, as opposed to a full baguette.

La moitié de [la] baguette means "the half of baguette" or "half the baguette", implying that we're talking about a specific baguette here, of which you'd want half.

The sentence here could be heard in a boulangerie, where you would ask for half a baguette, hence une demi-baguette.

I hope that's helpful!

À bientôt !