I think it is the end user who requests the support role to accept that they share what is on their screen.
Of course I understand that the support person would find it easier if they could always share the screen.
But I would not feel comfortable if someone out of nowhere asked me to share the screen with me.
You should always try to have a dialogue with your client and for me "screen sharing" should be the last option; how to ask someone to come home and help you.
If you can not help the client through the chat; Then, the service representative can suggest to the client to share the screen.
Helping someone is about making the client feel good about himself and the end result.
Some people may feel offended if they "jump the gun" and request a shared screen without a previous question.
So keep it in mind!