Demand. It's the only time of day / week when they can show such a programme without it eating into their primetime viewing figures. I think the Big 5 channels assume that everyone has some type of recording device so they can record these late night programmes and play them at any time of the day.
Hopefully with the 'on-demand' potential that visual media has for the future, there will be more dedicated channels and even downloadable content via digital / Satelite TV or Internet for deaf people.