I'm not sure this is true. The likelihood is that the contract for all the movies was signed before any of the movies, such that Radcliffe would be contractually obliged to finish the series, rather than holding development hostage at the last minute.
This is true of the first five films, but the later ones were separately negotiated
"Radcliffe found himself playing the lead role of Harry Potter in the anticipated family film, Harry Potter and the Philosopher's Stone, based on J.K. Rowling's popular novel, and signed on to star in the first five movies.
Once his contract was up, he signed another contract for $50 million to star in the final two films of the series."
