Utter nonsense.
There are many families who do not have access to a car, and often these are the poorest people in society.
I accept that bus drivers, and other transport workers, may wish to spend Christmas with their families.
However what do they do on Christmas Day?
Watch TV, browse the internet, go to the pub, use electricity, gas or water, need the emergency services.
All of these activities require other people to work on Christmas Day. My father was a policeman, and he had to work on Christmas Day sometimes. I don't remember feeling particularly deprived because of this.
And if you do drive somewhere in a car, what happens if it breaks down? Are you going to be stuck on the hard shoulder of a motorway until Boxing Day, because shouldn't the people who work for the AA and RAC be spending Christmas Day with their families.
The fact that some limited services do operate on Christmas Day shows that there is some demand for travel. Indeed National Express coaches operate several services on Christmas Day, from London at least, which they wouldn't do if they didn't think it was worth it.