I too found the single repetitive note to be jarring, discordant, and disturbing and I wanted it to end. But yet somehow I found the music was fitting to the scenes where it was used. It emoted claustrophobia and I felt I just wanted to escape - probably like Anne felt, too.
The majority of the film takes place in the palace, either in Anne's bedroom or in the court chambers. Anne is trapped in a life/role she is not suited for, in a building she can't escape, and in a body that is failing and racked with pain. Plus she is bored out of her mind, and likely has some psychological issues to deal with, as well. So that simple one note score seemed to exemplify and emphasize Anne's despair, torment, helplessness, etc. The score isn't pleasant but its effective.
I guess the main purpose of any film score is not to provide nice music to help us pass time while watching the movie. But instead to further under-score what's being communicated in the scenes themselves.
That was a very well thought out discourse. But, I believe the decibels utilized to broadcast the score was too much. And, the score itself was irritating. Surely, Anne was uncomfortable is her own skin and predicament. I understand your point that the score was unpleasant on purpose to project Anne's malaise on to the audience. I believe it could have been better and certainly toned down.
Queen Anne: I’m ready for the Russian ambassador.
Lady Sarah: Who did your makeup?
Queen Anne: We went for something dramatic. Do you like it?
Lady Sarah: You look like a badger.
Queen Anne: Oh.