Yes, panjandrum, I remember that in your post your personal view is expressed. But this view is very important to us because you are a native speaker and hence you feel the language better than any learner on Earth. I repeat that I was surprised at never hearing "accede to the throne" in films and never encountering it in books, though I have long known this collocation.Please remember that what I gave above was my personal view on this.
Despite Loob's assurance, that is no guarantee of general truth.
"Assume the throne" may well be even more popular than any of the others, despite that fact that I find it somewhat absurd.