Having not read Harry Potter I have no idea about Hagrid and the use of accent. I have, however, read Dracula and there are whole passages, pages upon pages of dialogue written in some Scottish sailor a cent that are totally unreadable.
Dracula was written in a period of time in which "phonetic" rendering of an accent was the accepted norm. It generally isn't, anymore (except maybe Irvine Welsh, who I find unreadable).
English is not a language even close to phonetically-rendered as normally written, and even native English speakers feature a wide variety of accents and pronunciations (think Jamaica, South Africa, Australia, Appalachia, Brooklyn, Boston Southies, Maine Downeasters, English Geordies, etc.).
If you don't believe this, say these words aloud:
bomb
comb
tomb
or, better yet:
tough
though
through
bought
cough
bough
An occasional little tweak might be effective, but comprehensive use of variant intended accent spellings is going to get hammered by just about any editor. A much more effect way of rendering speech from a character for whom English is not a thoroughly fluent tongue is by word choice.
caw