I see Doctor Who as the BBC equivalent to working on a Star Trek show.
It's more than just another show on the resume. It has a life after your stint is done. Fans, conventions, interviews, 10 year incremental anniversary specials, etc.
By the time Eccleston came around, this shouldn't have been a surprise that there's more Doctor Who stuff to do after you shoot your last episode.
Kind of like being a former Miss America, each one is expected to continue being a good role model and give a speech now and then.
Tom Baker did something similar for years. Got irritated with people who thought of him just as The Doctor, refused to appear in multi-Doctor episodes, etc.
In later years he admitted that was all a mistake, and that he was a fool to have acted like that. He said that in truth those years working on the show were the happiest of his life.
Eccleston, of course, famously hated his time on the show due to his personality clash with RTD.