Re: What problem are the certificates solving?
In the case of a browser, it doesn't know, a priori, what it is likely to be connecting to and a third party attestation is useful.
However, iPlayer (or whatever) knows exactly what it should be connecting to and the third party attestation offers nothing over what iPlayer could check for itself. At its most trivial, the app could contain the necessary certificate chain rather than rely on the one provided by the underlying system and an update to the app could update the necessary certificates.
Of course you have the slightly circular problem that if the app store certificates expire, you can't update the apps, but that's a problem the third party service provider doesn't have to work around itself.
I'm assuming the issue is that the APIs for some of these "smart" TV systems are in fact pretty minimal and don't offer you much beyond "render this URL as an H.264 video stream".
Biting the hand that feeds IT
