And Cook has scored more test runs opening the batting then anyone else in history... But can't be considered a great?
Depends what you mean by "great". As a batsman he has well-documented strengths, and he has well-documented weaknesses. He had a golden patch between 2010 and 2012 where he really was outstanding, but outside of that window he's been extremely inconsistent, even by the standards of an opener. He's also had some noticeably poor series whenever he comes up against genuinely quick bowling on quick decks. Statistically he's comparable to the likes of Gooch and Boycott, but its beyond argument that the average standard of bowling he has faced in the past decade has been considerably lower than at almost any previous point in history.
Would he have had as successful a career in the 80s and the 90s, given what we know about his weaknesses against pace? Its a valid question. I think if he and Atherton swapped eras, then Atherton would be retiring as England's leading test run scorer today.
His longevity is simultaneously impressive, but also a result of a) England's increasingly hectic schedule, and b) the limited pressure on his place due to a complete absence of alternative opening options since Strauss retired.