She claims fealty by right of blood, reigned as the crown of an extraordinarily cruel empire, and frequently interceded in the democratic government of Britain to protect her private interests.
Being in the Commonwealth doesn't mean "staying on" the British Empire - it just means belonging to a very, very loose trade block on which Britain temporarily exercised an outsized influence. Recent developments (like the inability of subsequent UK governments to replace Commonwealth leadership) have shown that even that influence has now gone. At this point the Commonwealth is little more than an administrative construct for trade-related issues.