Yes, wysiwig my DD has a similar issue to you - lots of thing going around in her head and so listening to something to get rid of the thoughts allows her brain to switch off.
But it is not really a "miracle cure", it helps a little. Like some of the previous posters, my DD has always had trouble getting to sleep and between the ages of 2 and 4 I got so frustrated as I could lie with her for 2 hours and like you Clover, very much resented the intrusion on my time. She is 12 now and still like this. It is just her I think and will probably be like this through adulthood. Therefore I think it is good to look at some strategies to help a little. We have gone from regular nights of 90 minutes lying awake at night down to about an hour now and 90 minutes is unusual. Still not ideal but better. And the meditations definitely help that.