I just checked, iPad has it (and using colour coding, as that has come up elsewhere in these threads). On Apple TV a subtitle menu appears in the time bar, but it doesn't seem to do anything in either the "Automatic" or "CC" options it gives?

CC is a bit of an Americanism, perhaps it is running more directly though some Apple playback code that is more particular about subtitle formats?

I suspect the ultimate case is probably low usage statistics not making it a priority. The icon / BBC logo didn't update at the same time as the iOS version, so I suspect its a separate codebase for some reason?