Ah, actually, I had not until you linked it in your post. So, D.C. Fontana was the catalyst (pun intended) for this story.
Purely supposition here, but I think if Niven had any idea Trek would later develop into powerhouse enterainment property it did, he might have resisted the pleas to include the Kzinti and the other Known Space elements. He possibly assumed in '73 that Trek would run a few years in syndication and then fade into obscurity.
Sincerely,
Bill