Why most of those Christmas songs were written by Jews

A new movie/dramatization/documentary celebrates the little-known factoid - which I did actually know, but had forgotten - that most of those schmaltzy, ultra-American, inescapable Christmas songs that take over stores, shopping centres, even whole radio networks for two months every year, were actually written by Jewish songwriters. Dreaming of a Jewish Christmas investigates how Christmas became a staple of Jewish songwriters who didn't even celebrate Christmas.
And we are not talking here about a few Chritmas songs: most of the famous ones that you'll know, and either love or hate, were penned by Jews. I failed to find a definitive list, but songs wholly or partially written by Jews include (Jewish writers in bold):

• White Christmas (Irving Berlin)
• The Christmas Song (Chestnuts Roasting) (Mel Tormé and Robert Wells)
• Rudolph the Red-Nosed Reindeer (Johnny Marks)
• Winter Wonderland (Felix Bernard and Richard B. Smith)
• The Christmas Waltz (Sammy Cahn and Julie Styne)
• Sleigh Ride (Leroy Anderson and Mitchell Parish)
• It's the Most Wonderful Time of the Year (George Wyle and Edward Pola)
• Silver Bells (Jay Livingston and Ray Evans)
• Rockin' Around the Christmas Tree (Johnny Marks)
• I'll Be Home for Christmas (Walter Kent and Buck Ram)
• A Holly Jolly Christmas (Johnny Marks)
• There's No Place Like Home for the Holidays (Robert Allen and Al Stillman)
• Have Yourself A Merry Little Christmas (Ralph Blane and Hugh Martin)
• Santa Claus Is Coming To Town (Fred Coots and Haven Gillespie)
• Let it Snow (Sammy Cahn and Julie Styne)
• Santa Baby (Joan Javits and Philip Springer)
• You're A Mean One Mr. Grinch (Albert Hague)
• Christmas (Baby, Please Come Home) (Jeff Barry, Ellie Greenwich and Phil Spector)
• Silver and Gold (Johnny Marks)
• Do You Hear What I Hear? (Noël Regny and Gloria Shanyne Baker)

And why, you ask? Well, no particular reason. It's just one of those odd cultural phenomena that seems like it should have a good, satisfying explanation but it really doesn't. It's not like a bunch of Jews set out to co-opt a popular Christian institution. It just so happens that many popular American songwriters in the post-War years happened to be Jewish, and songwriters would write whatever was popular, or whatever they were commissioned to write.
And it's not like these are deeply spiritual Christian songs. With the possible exception of Do You Hear What I Hear (which was actually written during the Cuban missile crisis as a peace song), they do not deal with "the Christmas story". They are not Christmas carols, which is a whole other genre of songs. They are generic songs about the Christmas time of year, as it is lived in America - winter, presents, parties, food, etc.
Which is why they have been taken up with such aplomb by schools in our politically correct, secular, inclusive times. Which I, as a secularist, should welcome. I just wish they were not so schmalzy and schlocky (good Jewish words both). And I wish they were not so ubiquitous and so pervasive.