The Graham Norton Show Channel

1: It's up to the source material to have captioning informaiton.

2: Music rights are often separate, and can be VERY EXPENSIVE. It's not unusual for music segments to be removed from repeats and syndicated versions of talk and variety shows.

With music, they would have to regularly pay to the record labels/artists the fee to use that material on a regular basis, like Spotify, broadcast radio and others have to do.  Most likely, they don't want to pay those fees.