I recently enquired if the BBC will be fixing the subtitle issue soon and got the following reply:
BBC iPlayer & BBC Sounds - Case number CAS-7793318-F3H2J7
Hello,
Thanks for getting in touch with BBC iPlayer Support Team about being unable to get subtitles on iPlayer on the Apple TV.
The subtitles used on the Apple TV are considerably different from others and so there is considerable challenge in making them available. This is why subtitles are available on all other platforms but not on this one. We do hope to do this at some point in future but there is no time frame for this unfortunately.
I can understand your frustration and rest assured that I will register your complaint on our dedicated feedback report, which is seen by the BBC iPlayer Product Team, including the BBC Accessibility team.
In the meantime, you could look into adapting your TV with another device such as a set-top box or streamer. Obviously, this isn't ideal, but I think it might be the only way you'll be able to get subtitles now. We cannot give any recommendations, but we do have a useful page here explaining your options:
https://www.bbc.co.uk/iplayer/help/questions/supported-devices/existing-device-help
Thanks again for getting in touch with us.
Rebekah Erskine
BBC iPlayer & BBC Sounds Support Team
https://www.bbc.co.uk/iplayer/help