If we're being honest, it's because the BBC is trying to navigate a small but annoying bunch of people who feel very strongly they should be able to shout out homophobic slurs every Christmas and don't want to be told they've been possibly been offending people for years by doing so.
If you read the BBC statement -
A BBC spokesman said: "We know the song is considered a Christmas classic and we will continue to play it this year, with our radio stations choosing the version of the song most relevant for their audience."
I would suggest the most revealing part would be "this year", and that Radio 2 will standalone in its usage before probably moving on in the future.