In a value-creation bridge, why is the EBITDA-growth contribution typically valued at the ENTRY multiple while the multiple-expansion contribution is valued at the EXIT EBITDA?

It's a convention to avoid double-counting the cross term (ΔEBITDA × Δmultiple). Exit EV − Entry EV = (ΔEBITDA × entry multiple) + (Δmultiple × exit EBITDA). The growth bucket holds the multiple fixed at entry; the multiple bucket then applies the full multiple change to the larger exit EBITDA, which absorbs the cross term. Equivalently you can value growth at exit multiple and multiple change at entry EBITDA — the point is to assign the cross term consistently to one bucket so the layers sum exactly to total EV change.