Thank you for contacting us. We are glad that you are a happy Blizz customer.
The presenter's chat window is seen gray by the participants, when the presenter is using Windows 10, this is a bug with this operating system and the developers are already working on finding a solution.
If the presenter uses a different operating system, the chat window is only visible for the presenter. Your feedback is very important and I will be glad to forward your comments to our Blizz Product Management in regards to your request to be able to move the window.
Don't hesitate to contact us if you have any further questions.
Have a good weekend.
Thank you for adding this additional feedback.
Unfortunately, I cannot yet provide you a date for the implementation of a different use to the chat window. Rest assured however that our Blizz Product Management is already aware of your feedback and that of other customers in regards to this request.