I contacted ITVX support and got the following
Thanks for contacting ITVX, I hope you are well. 🙂
In regards to Roku being built in a TV and a Roku stick being the same they are correct.
On our supported device pages it clearly states on the Live TV section -
"The live TV feature is currently available only on Amazon Fire TV, Android TV, NowTV/Roku streaming players, Samsung Smart TVs, Sky Glass and Sky Stream puck, Xbox One/S/X and Xbox Series X/S.
Sometimes a show will only have television rights and not online rights. If this happens you will receive a message saying the programme is unavailable - don’t worry, this isn’t a technical fault. "
So this would not be an ITVX issue because we clearly state our live TV feature is available on Roku streaming players whether it's built in or a stick we still support these devices with our live TV feature.
From the description you have given this sounds like it's do to do with the TV or Roku and you'd be best contacting them in regards to this issue.
I know this is not the answer you were looking for but I hope it has somewhat cleared up any misunderstanding.
So a built in Roku is supported. As I have this problem on both Hisense and TCL Roku TV's the only common thing is Roku.
How do I progress this with them as nobody from Roku has joined in this thread.