Why did he keep the Woltz story? Just because the horse in the bed was so spectacular?
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Yes, but not just because it was graphihc and spectacular. See below:
We need the wedding scene to understand the family. The the story starts to unfold when Sollozzo meets the Corleones.
If we need the Woltz story then it is 1) to show how the Corleones work at that time and 2) how powerful they are. However, we know that already from the wedding scene: 1) The Luca/Johnny story, 2) the Corleones can buy a new law from the congress.
The Woltz episode has no further impact on the development of the film. But: 1) and 2) are just stories, with little dramatic impact. The Woltz scene shows the crude power that backs up Vito's maneuvering and diplomacy. It shows that Vito can reach across the country and use violence to get his way, even if it's only to satisfy his ne'er-do-well godson. But there's also a business interest: Vito controls or influences Hollywood labor unions and needs to assert his power over Woltz to maintain his credibility 3,000 miles from his home.
