Very interesting observation, I am a fan of John Scott Trotter while I agree that Bing shouldn’t relied so much on the same arranger. But Trotter had an immense versality.
There is some true to the accusation that he had a tendency to be repetitive, Lionel Pairpoint mentioned a lot of similarities between Trotter’s arrangement but this one was not included. But still his work was so important, he was one of the most prolific arrangers of his time and able to deal with an immense workload without producing cheap unimaginative arrangements, all his work had a basic quality though not always maintaining the same level.
Bing Crosby would be the best judge of that and according to Lionel Pairpoints book that is available on our club’s website Bing said that Trotter was “very good with a mervellous taste….(and his arrangements were) never obtrusive.. always in good taste’.”
I never had noticed it before you posted It and you are right it is the same intro. Trotter did the arrangement on both and it is a Christmas themed intro that suits well both songs. He was often reusing some parts of his arrangements on radio tracks. I guess it was not easy to detect them then cause radio show weren’t easily available and it would be rare to hear both together and almost impossible to remember it. After all he was doing hundreds of arrangements each year for Bing’s radio show.
 

I do not now anything about subconstracting arrangments but I guess that is is almost human imposible for one single musician to arrange so many songs per week for the radio shows that Bing was doing plus the Decca recordings. Bing always spoke highly of him and he was indeed a talented man even if his legacy is not the one he deserved.