I don't think we can blame Alice for this. Ioan was a way bigger star than Alice even back then, and wasn't he in the running to be James Bond?I would say the move to LA was Alice driven rather than Ioan seeing himself as the next big thing.
He had fulfilled the first steps of the "UK actor who makes it big in Hollywood" method - having hugely successful and well-reviewed TV shows in the UK (with Hornblower being exported to the world), and even already having a small part in a massive blockbuster film.
He was handsome, RADA-trained, talented, and ambitious. His peers were Damian Lewis and Matthew Rhys. Of course he was always going to try for Hollywood.